Where do these special functions actually get used? This page cross-tabulates the function families × application areas in the literature we've indexed. For each area (image processing, signal processing, medical imaging, etc.), the list shows every function family with at least one citation from a paper in that area - the candidate "patterns" the project is hunting.
The application tags are derived by keyword scanning every paper's abstract + first 5 pages. Conservative: a paper is tagged only if a domain-specific phrase appears (e.g. "image processing", "CT scan", "Rabotnov").
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 2024 · 2024 |
| Janowski S*[A,B] extremal | Janowski | - | 2024 · 2024 |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 2024 · 2024 |
| Mocanu α-convex | Mocanu | - | 2024 · 2024 |
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| Cusp-domain family demo (z + z²/4 - z³/8) | Cusp Domain | z + z**2/4 - z**3/8 | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Mittag-Leffler E_α | Mittag-Leffler | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Wright φ(α,β; z) | Wright | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 2023 · 2021 · 2019 |
| Janowski S*[A,B] extremal | Janowski | - | 2023 · 2022 · 2019 |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 2023 · 2021 · 2019 |
| Mocanu α-convex | Mocanu | - | 2023 · 2021 · 2019 |
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Miller-Ross family demo (z·E_{1,2}(z)) | Fractional | z*(exp(z)-1)/z + z*0 | 1 paper → |
| Ruscheweyh family R(λ) | Ruscheweyh | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 2023 · 2021 · 2020 · 2019 · 2019 · 2015 · 2014 |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 2023 · 2021 · 2020 · 2019 · 2019 · 2015 · 2014 |
| Mocanu α-convex | Mocanu | - | 2024 · 2021 · 2014 |
| Ruscheweyh family R(λ) | Ruscheweyh | - | 2023 · 2011 |
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Wright φ(α,β; z) | Wright | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Mittag-Leffler E_α | Mittag-Leffler | - | 2019 · 2018 |
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Miller-Ross family demo (z·E_{1,2}(z)) | Fractional | z*(exp(z)-1)/z + z*0 | 1 paper → |
| Rabotnov-family demo (z + z²/2 + z³/6) | Fractional | z + z**2/2 + z**3/6 | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Wright φ(α,β; z) | Wright | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Modified Bessel I_ν | Bessel | - | 2025 · 2016 |
| Normalized Bessel J_ν | Bessel | - | 2025 · 2016 |
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 2026 · 2016 |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 2026 · 2016 |
| Janowski S*[A,B] extremal | Janowski | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Mittag-Leffler E_α | Mittag-Leffler | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Wright φ(α,β; z) | Wright | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Modified Bessel I_ν | Bessel | - | 2025 · 2017 |
| Normalized Bessel J_ν | Bessel | - | 2025 · 2017 |
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 1 paper → |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 1 paper → |
| Lommel s_{μ,ν}(z) normalized (ν=1/2) | Lommel | - | 1 paper → |
| Struve H_ν (normalized) | Struve | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Modified Bessel I_ν | Bessel | - | 1 paper → |
| Normalized Bessel J_ν | Bessel | - | 1 paper → |
| ₂F₁(a, b; c; z) — Gauss hypergeometric | Hypergeometric | - | 1 paper → |
| Janowski S*[A,B] extremal | Janowski | - | 1 paper → |
| ₁F₁(a; c; z) — Kummer confluent hypergeometric | Hypergeometric | - | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Cusp-domain family demo (z + z²/4 - z³/8) | Cusp Domain | z + z**2/4 - z**3/8 | 1 paper → |
| Miller-Ross family demo (z·E_{1,2}(z)) | Fractional | z*(exp(z)-1)/z + z*0 | 1 paper → |
| Mocanu α-convex | Mocanu | - | 1 paper → |
| Rabotnov-family demo (z + z²/2 + z³/6) | Fractional | z + z**2/2 + z**3/6 | 1 paper → |
| Family | Group | Closed form | Cited by |
|---|---|---|---|
| Miller-Ross family demo (z·E_{1,2}(z)) | Fractional | z*(exp(z)-1)/z + z*0 | 1 paper → |
| Mocanu α-convex | Mocanu | - | 1 paper → |
| Rabotnov-family demo (z + z²/2 + z³/6) | Fractional | z + z**2/2 + z**3/6 | 1 paper → |
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