qualia_core_db/solvers/special_functions/mod.rs
1//! **Special functions** (Gap analysis §3.5) — beyond the Gamma/erf/incomplete family
2//! already in [`crate::solvers::statistics::distributions::special`].
3//!
4//! * [`orthogonal`] — Legendre, Chebyshev (T/U), Hermite, Laguerre polynomials by
5//! their three-term recurrences.
6//! * [`bessel`] — Bessel `J`/`Y` and modified `I`/`K` (integer order): convergent
7//! series for the order-0 building blocks, the Wronskian for order 1, then the
8//! standard recurrences.
9//! * [`airy`] — Airy `Ai`/`Bi` via their Maclaurin series.
10//! * [`zeta`] — Riemann ζ(s) for real `s > 1` via Euler–Maclaurin acceleration.
11//!
12//! Domain-restricted functions fail closed (`Option`/`None`) rather than return a
13//! fabricated value (e.g. `Y_n`/`K_n` require `x > 0`; ζ requires `s > 1`). The series
14//! methods are accurate for moderate arguments; the convergence regime is documented
15//! per function.
16
17pub mod airy;
18pub mod bessel;
19pub mod orthogonal;
20pub mod zeta;
21
22pub use airy::{airy_ai, airy_bi};
23pub use bessel::{bessel_i, bessel_j, bessel_k, bessel_y};
24pub use orthogonal::{chebyshev_t, chebyshev_u, hermite, laguerre, legendre};
25pub use zeta::zeta;