One entry per mathematical family, deduplicated across naming variants and grouped by type. Parametric families collapse many historical singletons into a single entity with a parameter space.
| Modified Bessel I_ν | - | 17 proven 2 disproven applied parametric (1) | 19 · 25 |
| Normalized Bessel J_ν | - | 27 proven 4 disproven applied parametric (1) | 33 · 66 |
| Miller-Ross family demo (z·E_{1,2}(z)) | z*(exp(z)-1)/z + z*0 | 1 proven applied | 1 · 1 |
| Rabotnov-family demo (z + z²/2 + z³/6) | z + z**2/2 + z**3/6 | 1 proven applied | 1 · 1 |
| ₂F₁(a, b; c; z) — Gauss hypergeometric | - | 9 proven 4 disproven applied parametric (3) | 13 · 22 |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | - | 19 proven 2 disproven applied parametric (2) | 21 · 36 |
| Cusp-domain family demo (z + z²/4 - z³/8) | z + z**2/4 - z**3/8 | 1 proven applied | 1 · 1 |
| Janowski S*[A,B] extremal | - | 8 proven 10 disproven applied parametric (2) | 20 · 38 |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | - | 14 disproven applied parametric (1) | 14 · 23 |
| Mittag-Leffler E_α | - | 26 proven 13 disproven applied parametric (1) | 38 · 78 |
| Mocanu α-convex | - | 14 proven 7 disproven applied parametric (1) | 21 · 30 |
| Ruscheweyh family R(λ) | - | 23 disproven applied parametric (1) | 23 · 35 |
| Struve H_ν (normalized) | - | 11 proven applied parametric (1) | 16 · 34 |
| Wright φ(α,β; z) | - | 18 proven 27 disproven applied parametric (2) | 45 · 60 |