UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{4} + 1e-07\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
659,385 boxes
·
329,693 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{4} + 1e-07\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
655,217 boxes
·
327,609 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-07\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
661,597 boxes
·
330,799 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-07\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
785,639 boxes
·
392,820 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-07\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
1,079,207 boxes
·
539,604 leaves
UNDER_REVIEW
known theorem
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.01\)
over Bean S*_𝔅,
\(\varphi(z)=\sqrt{1+\tanh z}\)
Kumar & Verma 2025 (Filomat)
10,987 boxes
·
5,494 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Bell S*_B,
\(\varphi(z)=e^{e^{z}-1}\)
46,672,735 boxes
·
23,336,368 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Bell S*_B,
\(\varphi(z)=e^{e^{z}-1}\)
564,869 boxes
·
282,435 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Bell S*_B,
\(\varphi(z)=e^{e^{z}-1}\)
546,085 boxes
·
273,043 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{23}{24} + 1e-06\)
over Bell S*_B,
\(\varphi(z)=e^{e^{z}-1}\)
4,123 boxes
·
2,062 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{17}{16} + 1e-06\)
over Bell S*_B,
\(\varphi(z)=e^{e^{z}-1}\)
2,311 boxes
·
1,156 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{2}{3} + 1e-06\)
over Cardioid S*_C,
\(\varphi(z)=1+\tfrac{4z}{3}+\tfrac{2z^{2}}{3}\)
559,217 boxes
·
279,609 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{2}{3} + 1e-06\)
over Cardioid S*_C,
\(\varphi(z)=1+\tfrac{4z}{3}+\tfrac{2z^{2}}{3}\)
577,471 boxes
·
288,736 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{2}{3} + 1e-06\)
over Cardioid S*_C,
\(\varphi(z)=1+\tfrac{4z}{3}+\tfrac{2z^{2}}{3}\)
1,142,741 boxes
·
571,371 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{27}{32} + 1e-06\)
over Cardioid S*_C,
\(\varphi(z)=1+\tfrac{4z}{3}+\tfrac{2z^{2}}{3}\)
7,839 boxes
·
3,920 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|A_4| \le \tfrac{368}{81} + 1e-06\)
over Cardioid S*_C,
\(\varphi(z)=1+\tfrac{4z}{3}+\tfrac{2z^{2}}{3}\)
2,329 boxes
·
1,165 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Cardioid S*_℘,
\(\varphi(z)=1+z\,e^{z}\)
46,485,173 boxes
·
23,242,587 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Cardioid S*_℘,
\(\varphi(z)=1+z\,e^{z}\)
1,493,955 boxes
·
746,978 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Cardioid S*_℘,
\(\varphi(z)=1+z\,e^{z}\)
1,455,661 boxes
·
727,831 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{5}{6} + 1e-06\)
over Cardioid S*_℘,
\(\varphi(z)=1+z\,e^{z}\)
6,363 boxes
·
3,182 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{7}{6} + 1e-06\)
over Cardioid S*_℘,
\(\varphi(z)=1+z\,e^{z}\)
3,567 boxes
·
1,784 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Cissoid S*_{cs},
\(\varphi(z)=1+\frac{z}{(1-z)(1+z/3)}\)
1,583,769 boxes
·
791,885 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Cissoid S*_{cs},
\(\varphi(z)=1+\frac{z}{(1-z)(1+z/3)}\)
1,300,267 boxes
·
650,134 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Cissoid S*_{cs},
\(\varphi(z)=1+\frac{z}{(1-z)(1+z/3)}\)
1,485,565 boxes
·
742,783 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{37}{48} + 1e-06\)
over Cissoid S*_{cs},
\(\varphi(z)=1+\frac{z}{(1-z)(1+z/3)}\)
3,295 boxes
·
1,648 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{11}{12} + 1e-06\)
over Cissoid S*_{cs},
\(\varphi(z)=1+\frac{z}{(1-z)(1+z/3)}\)
2,823 boxes
·
1,412 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
240,455 boxes
·
120,228 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
212,983 boxes
·
106,492 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
212,261 boxes
·
106,131 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
212,153 boxes
·
106,077 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
248,973 boxes
·
124,487 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.01\)
over Cosh-sqrt,
\(\varphi(z)=\cosh\sqrt{z}\)
9,943 boxes
·
4,972 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Crescent,
\(\varphi(z)=z+\sqrt{1+z^{2}}\)
505,493 boxes
·
252,747 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Crescent,
\(\varphi(z)=z+\sqrt{1+z^{2}}\)
491,725 boxes
·
245,863 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Crescent,
\(\varphi(z)=z+\sqrt{1+z^{2}}\)
574,155 boxes
·
287,078 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{13}{12} + 1e-06\)
over Crescent,
\(\varphi(z)=z+\sqrt{1+z^{2}}\)
2,919 boxes
·
1,460 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{3}{8} + 1e-07\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
928,369 boxes
·
464,185 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{3}{8} + 1e-07\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
770,713 boxes
·
385,357 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{3}{8} + 1e-07\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
697,357 boxes
·
348,679 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{8} + 1e-07\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
825,453 boxes
·
412,727 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{8} + 1e-07\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
1,225,845 boxes
·
612,923 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{7}{24} + 1e-06\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
23,979 boxes
·
11,990 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{5}{32} + 0.01\)
over Epicycloid S*_{3ℒ},
\(\varphi(z)=1+\tfrac{3z}{4}+\tfrac{z^{3}}{4}\)
9,983 boxes
·
4,992 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{3}{7} + 1e-06\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
574,341 boxes
·
287,171 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{3}{7} + 1e-07\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
873,609 boxes
·
436,805 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{3}{7} + 1e-07\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
758,381 boxes
·
379,191 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{7} + 1e-07\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
978,541 boxes
·
489,271 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{7} + 1e-07\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
1,779,045 boxes
·
889,523 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{13}{24} + 1e-06\)
over Epicycloid S*_{6ℒ},
\(\varphi(z)=1+\tfrac{6z}{7}+\tfrac{z^{6}}{7}\)
4,455 boxes
·
2,228 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Exponential S*_e,
\(\varphi(z)=e^{z}\)
505,493 boxes
·
252,747 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Exponential S*_e,
\(\varphi(z)=e^{z}\)
491,725 boxes
·
245,863 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Exponential S*_e,
\(\varphi(z)=e^{z}\)
574,155 boxes
·
287,078 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{23}{48} + 1e-06\)
over Exponential S*_e,
\(\varphi(z)=e^{z}\)
14,851 boxes
·
7,426 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|A_4| \le \tfrac{31}{18} + 1e-06\)
over Exponential S*_e,
\(\varphi(z)=e^{z}\)
3,719 boxes
·
1,860 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{5}{12} + 1e-06\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
530,163 boxes
·
265,082 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{5}{12} + 1e-07\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
855,995 boxes
·
427,998 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{5}{12} + 1e-07\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
750,353 boxes
·
375,177 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{5}{12} + 1e-07\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
947,769 boxes
·
473,885 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{5}{12} + 1e-07\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
1,620,345 boxes
·
810,173 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{1}{2} + 1e-06\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
4,967 boxes
·
2,484 leaves
UNDER_REVIEW
1 in literature
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{3}{16} + 0.02\)
over Four-leaf S*_{4L},
\(\varphi(z)=1+\tfrac{5z}{6}+\tfrac{z^{5}}{6}\)
9,671 boxes
·
71,753 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_2a_3| \le \tfrac{3}{4}\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3| \le \tfrac{3}{4}\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
45 boxes
·
23 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2}\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
505,493 boxes
·
252,747 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
491,725 boxes
·
245,863 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
574,155 boxes
·
287,078 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le \tfrac{5}{4} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
7 boxes
·
4 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
21,339 boxes
·
10,670 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le 1 + 1e-06\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
2,303 boxes
·
1,152 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le \tfrac{5}{4}\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{1}{4}\)
over Janowski S*[1/2,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{1}{2},\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_2a_3| \le \tfrac{5}{8}\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3| \le \tfrac{5}{8}\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{5}{8} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
81 boxes
·
41 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
593,153 boxes
·
296,577 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
424,987 boxes
·
212,494 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
441,597 boxes
·
220,799 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
767,533 boxes
·
383,767 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le \tfrac{11}{8} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
7 boxes
·
4 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{15}{16} + 1e-06\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
2,963 boxes
·
1,482 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le \tfrac{11}{8}\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{1}{4}\)
over Janowski S*[3/4,-1/4],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=\tfrac{3}{4},\ B=-\tfrac{1}{4}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_2a_3| \le 1\)
over Janowski S*[0,-1],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=0,\ B=-1\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3| \le 1\)
over Janowski S*[0,-1],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=0,\ B=-1\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le 1\)
over Janowski S*[0,-1],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=0,\ B=-1\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{1}{4}\)
over Janowski S*[0,-1],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=0,\ B=-1\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_2a_3| \le \tfrac{9}{4}\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3| \le \tfrac{3}{2}\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{3}{2} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
17 boxes
·
9 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{15}{16} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
123 boxes
·
62 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
575,791 boxes
·
287,896 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
604,613 boxes
·
302,307 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
90,330,087 boxes
·
45,165,044 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le 3 + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
5 boxes
·
3 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{5}{4} + 1e-06\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
4,695 boxes
·
2,348 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le 3\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{3}{8}\)
over Janowski S*[1,-1/2],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=-\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_2a_3| \le \tfrac{1}{2}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3| \le \tfrac{1}{2}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{2}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
429,353 boxes
·
214,677 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
358,741 boxes
·
179,371 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
510,565 boxes
·
255,283 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le \tfrac{3}{2} + 1e-06\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
5 boxes
·
3 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{5}{6} + 1e-06\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
3,907 boxes
·
1,954 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le \tfrac{3}{2}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{1}{4}\)
over Janowski S*[1,0],
\(\varphi(z)=\frac{1+Az}{1+Bz},\ A=1,\ B=0\)
0 boxes
·
0 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
212,427 boxes
·
106,214 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
211,615 boxes
·
105,808 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
213,339 boxes
·
106,670 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
252,715 boxes
·
126,358 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
345,703 boxes
·
172,852 leaves
UNDER_REVIEW
known theorem
7 in literature
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.01\)
over Lemniscate S*_L,
\(\varphi(z)=\sqrt{1+z}\)
Lee, Ravichandran & Supramaniam 2013 (#455)
10,563 boxes
·
5,282 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{3}{10} + 1e-06\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
330,771 boxes
·
165,386 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{3}{10} + 1e-06\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
282,521 boxes
·
141,261 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{3}{10} + 1e-06\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
252,225 boxes
·
126,113 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{10} + 1e-06\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
264,957 boxes
·
132,479 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{10} + 1e-06\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
320,033 boxes
·
160,017 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{3}{32} + 0.02\)
over Limaçon S*(s=3/10),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{3}{10}\)
7,555 boxes
·
170,818 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Limaçon S*(s=1/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{1}{2}\)
593,153 boxes
·
296,577 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Limaçon S*(s=1/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{1}{2}\)
424,987 boxes
·
212,494 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Limaçon S*(s=1/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{1}{2}\)
441,597 boxes
·
220,799 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Limaçon S*(s=1/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{1}{2}\)
767,533 boxes
·
383,767 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{23}{24} + 1e-06\)
over Limaçon S*(s=1/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{1}{2}\)
2,639 boxes
·
1,320 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Limaçon S*(s=√2/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{\sqrt{2}}{2}\)
2,775 boxes
·
1,388 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le sqrt(2)/2 + 1e-06\)
over Limaçon S*(s=√2/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{\sqrt{2}}{2}\)
536,767 boxes
·
268,384 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le sqrt(2)/2 + 1e-06\)
over Limaçon S*(s=√2/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{\sqrt{2}}{2}\)
616,483 boxes
·
308,242 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Limaçon S*(s=√2/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{\sqrt{2}}{2}\)
6,447 boxes
·
3,224 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{5}{6} + 1e-06\)
over Limaçon S*(s=√2/2),
\(\varphi(z)=(1+sz)^{2},\ s=\tfrac{\sqrt{2}}{2}\)
8,391 boxes
·
4,196 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Nephroid S*_{Ne},
\(\varphi(z)=1+z-\tfrac{z^{3}}{3}\)
429,353 boxes
·
214,677 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Nephroid S*_{Ne},
\(\varphi(z)=1+z-\tfrac{z^{3}}{3}\)
358,741 boxes
·
179,371 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Nephroid S*_{Ne},
\(\varphi(z)=1+z-\tfrac{z^{3}}{3}\)
510,565 boxes
·
255,283 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{23}{24} + 1e-06\)
over Nephroid S*_{Ne},
\(\varphi(z)=1+z-\tfrac{z^{3}}{3}\)
3,451 boxes
·
1,726 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
36,194,331 boxes
·
18,097,166 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
1,336,707 boxes
·
668,354 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
1,286,205 boxes
·
643,103 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
1,485,119 boxes
·
742,560 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{7}{12} + 1e-06\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
11,003 boxes
·
5,502 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{11}{12} + 1e-06\)
over Non-convex S*_{nc},
\(\varphi(z)=\frac{1+z}{\cos z}\)
3,427 boxes
·
1,714 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Starlike of order 1/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{4}\)
656,729 boxes
·
328,365 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Starlike of order 1/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{4}\)
829,403 boxes
·
414,702 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Starlike of order 1/2,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{2}\)
564,869 boxes
·
282,435 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Starlike of order 1/2,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{2}\)
546,085 boxes
·
273,043 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le 1 + 1e-06\)
over Starlike of order 1/2,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{2}\)
5,627 boxes
·
2,814 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-\tfrac12 a_2a_3| \le \tfrac{1}{2} + 1e-06\)
over Starlike of order 1/2,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{2}\)
41,563 boxes
·
20,782 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le 1 + 1e-06\)
over Starlike of order 1/2,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{1}{2}\)
3,711 boxes
·
1,856 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
13,986,531 boxes
·
6,993,266 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
378,521 boxes
·
189,261 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
300,021 boxes
·
150,011 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
330,577 boxes
·
165,289 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{5}{16} + 1e-06\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
10,459 boxes
·
5,230 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.02\)
over Starlike of order 3/4,
\(\varphi(z)=\frac{1+(1-2\alpha)z}{1-z},\ \alpha=\tfrac{3}{4}\)
9,443 boxes
·
170,823 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le 4/pi**2 + 1e-06\)
over Parabolic S_p,
\(\varphi(z)=1+\tfrac{2}{\pi^{2}}\log^{2}\tfrac{1+\sqrt z}{1-\sqrt z}\)
545,823 boxes
·
272,912 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le 4/pi**2 + 1e-06\)
over Parabolic S_p,
\(\varphi(z)=1+\tfrac{2}{\pi^{2}}\log^{2}\tfrac{1+\sqrt z}{1-\sqrt z}\)
418,917 boxes
·
209,459 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le 4/pi**2 + 1e-06\)
over Parabolic S_p,
\(\varphi(z)=1+\tfrac{2}{\pi^{2}}\log^{2}\tfrac{1+\sqrt z}{1-\sqrt z}\)
464,471 boxes
·
232,236 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{11}{24} + 1e-06\)
over Parabolic S_p,
\(\varphi(z)=1+\tfrac{2}{\pi^{2}}\log^{2}\tfrac{1+\sqrt z}{1-\sqrt z}\)
7,051 boxes
·
3,526 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{13}{24} + 1e-06\)
over Parabolic S_p,
\(\varphi(z)=1+\tfrac{2}{\pi^{2}}\log^{2}\tfrac{1+\sqrt z}{1-\sqrt z}\)
3,931 boxes
·
1,966 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
25,673,687 boxes
·
12,836,844 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
1,130,073 boxes
·
565,037 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
946,145 boxes
·
473,073 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
1,330,029 boxes
·
665,015 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
53,035,473 boxes
·
26,517,737 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{29}{32} + 1e-06\)
over Petal S*_ρ,
\(\varphi(z)=1+\sinh^{-1}z\)
2,287 boxes
·
1,144 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le 9/2 - 3*sqrt(2) + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
81 boxes
·
41 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le 15/4 - 5*sqrt(2)/2 + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
3,357 boxes
·
1,679 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le -1/2 + sqrt(2)/2 + 0.001\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
57,578,165 boxes
·
28,789,083 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le -1/2 + sqrt(2)/2 + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
291,131 boxes
·
145,566 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le -1/2 + sqrt(2)/2 + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
255,267 boxes
·
127,634 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 2\, a_2^{2}| \le -1/2 + sqrt(2)/2 + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
277,173 boxes
·
138,587 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{5}{32} + 1e-06\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
19,851 boxes
·
9,926 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le 3/4 - sqrt(2)/2 + 0.01\)
over Rational S*_R,
\(\varphi(z)=1+\frac{z(k+z)}{k(k-z)},\ k=1+\sqrt2\)
11,111 boxes
·
5,556 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
215,915 boxes
·
107,958 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
212,427 boxes
·
106,214 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
212,217 boxes
·
106,109 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
212,947 boxes
·
106,474 leaves
UNDER_REVIEW
2 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
253,387 boxes
·
126,694 leaves
UNDER_REVIEW
known theorem
2 in literature
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.01\)
over Sigmoid S*_{SG},
\(\varphi(z)=\frac{2}{1+e^{-z}}\)
Riaz, Raza & Thomas 2022 (Forum Math.)
9,399 boxes
·
4,700 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Sine S*_{\sin},
\(\varphi(z)=1+\sin z\)
429,353 boxes
·
214,677 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Sine S*_{\sin},
\(\varphi(z)=1+\sin z\)
358,741 boxes
·
179,371 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Sine S*_{\sin},
\(\varphi(z)=1+\sin z\)
510,565 boxes
·
255,283 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{29}{32} + 1e-06\)
over Sine S*_{\sin},
\(\varphi(z)=1+\sin z\)
2,283 boxes
·
1,142 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|A_4| \le \tfrac{47}{18} + 1e-06\)
over Sine S*_{\sin},
\(\varphi(z)=1+\sin z\)
2,009 boxes
·
1,005 leaves
UNDER_REVIEW
22 in literature
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le 1 + 1e-06\)
over Starlike S*,
\(\varphi(z)=\frac{1+z}{1-z}\)
765,983 boxes
·
382,992 leaves
UNDER_REVIEW
known theorem
22 in literature
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le 1 + 0.0001\)
over Starlike S*,
\(\varphi(z)=\frac{1+z}{1-z}\)
Fekete–Szegő 1933 (classical)
3,113,875 boxes
·
1,556,938 leaves
UNDER_REVIEW
known theorem
closed-form engine
stored claim ·
\(|A_3|=|2a_2^{2}-a_3| \le 5\)
over Starlike S*,
\(\varphi(z)=\frac{1+z}{1-z}\)
Reduces to Fekete–Szegő (μ=2); |A₃| ≤ 5 sharp for S*
0 boxes
·
0 leaves
UNDER_REVIEW
known theorem
closed-form engine
stored claim ·
\(|\gamma_2| \le \tfrac{1}{2}\)
over Starlike S*,
\(\varphi(z)=\frac{1+z}{1-z}\)
|γₙ| ≤ 1/n for S* (classical)
0 boxes
·
0 leaves
UNDER_REVIEW
known theorem
dag engine
stored claim ·
\(|a_2a_3-a_4| \le 2 + 1e-06\)
over Starlike S*,
\(\varphi(z)=\frac{1+z}{1-z}\)
Generalized Zalcman, Ravichandran–Verma 2016 (|aₙaₘ−a_{n+m−1}| ≤ (n−1)(m−1) = 2)
6,619 boxes
·
3,310 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
25,673,687 boxes
·
12,836,844 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
1,130,073 boxes
·
565,037 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
946,145 boxes
·
473,073 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-07\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
1,330,029 boxes
·
665,015 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
53,035,473 boxes
·
26,517,737 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{23}{24} + 1e-06\)
over Strip S*_τ,
\(\varphi(z)=1+\arctan z\)
3,579 boxes
·
1,790 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
281,885 boxes
·
140,943 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
243,289 boxes
·
121,645 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
213,877 boxes
·
106,939 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
211,915 boxes
·
105,958 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{4} + 1e-06\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
240,333 boxes
·
120,167 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{16} + 0.01\)
over Strongly starlike SS*(1/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{4}\)
11,683 boxes
·
5,842 leaves
UNDER_REVIEW
closed-form engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2}\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
0 boxes
·
0 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
505,493 boxes
·
252,747 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
491,725 boxes
·
245,863 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
574,155 boxes
·
287,078 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{7}{12} + 1e-06\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
11,003 boxes
·
5,502 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{11}{12} + 1e-06\)
over Strongly starlike SS*(1/2),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{1}{2}\)
3,427 boxes
·
1,714 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Strongly starlike SS*(3/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{3}{4}\)
823,797 boxes
·
411,899 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Strongly starlike SS*(3/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{3}{4}\)
631,565 boxes
·
315,783 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{3}{4} + 1e-06\)
over Strongly starlike SS*(3/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{3}{4}\)
1,080,961 boxes
·
540,481 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4| \le \tfrac{85}{48} + 1e-06\)
over Strongly starlike SS*(3/4),
\(\varphi(z)=\left(\frac{1+z}{1-z}\right)^{\beta},\ \beta=\tfrac{3}{4}\)
2,669 boxes
·
1,335 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Tanh S*_{\tanh},
\(\varphi(z)=1+\tanh z\)
429,353 boxes
·
214,677 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Tanh S*_{\tanh},
\(\varphi(z)=1+\tanh z\)
358,741 boxes
·
179,371 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{1}{2} + 1e-06\)
over Tanh S*_{\tanh},
\(\varphi(z)=1+\tanh z\)
510,565 boxes
·
255,283 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{23}{24} + 1e-06\)
over Tanh S*_{\tanh},
\(\varphi(z)=1+\tanh z\)
3,451 boxes
·
1,726 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0\, a_2^{2}| \le \tfrac{2}{5} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
493,041 boxes
·
246,521 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.25\, a_2^{2}| \le \tfrac{2}{5} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
384,493 boxes
·
192,247 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-\tfrac12 a_2^{2}| \le \tfrac{2}{5} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
338,481 boxes
·
169,241 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3 - 0.75\, a_2^{2}| \le \tfrac{2}{5} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
412,621 boxes
·
206,311 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_3-a_2^{2}| \le \tfrac{2}{5} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
699,993 boxes
·
349,997 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_4-2a_2a_3| \le \tfrac{7}{16} + 1e-06\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
6,183 boxes
·
3,092 leaves
UNDER_REVIEW
dag engine
stored claim ·
\(|a_2a_4-a_3^{2}| \le \tfrac{1}{6} + 0.02\)
over Three-leaf,
\(\varphi(z)=1+\tfrac{4z}{5}+\tfrac{z^{4}}{5}\)
10,935 boxes
·
68,943 leaves