numra-special

Special mathematical functions for the Numra workspace — gamma, error functions, Bessel, elliptic integrals, Airy, hypergeometric, orthogonal polynomials, zeta, and more.

A compact, native-Rust library of special functions sufficient to back the distribution PDFs in numra-stats, the fractional-derivative analytics in numra-fde, and the analytical reference solutions used throughout the workspace's tests.

Example

use numra_special::{erf, gamma};

// Γ(1/2) = √π
assert!((gamma(0.5_f64) - std::f64::consts::PI.sqrt()).abs() < 1e-10);

// erf(1) ≈ 0.8427
assert!((erf(1.0_f64) - 0.8427007929_f64).abs() < 1e-8);

What's in this crate

• Gamma family: gamma, lgamma, digamma, beta, gammainc, gammaincc, betainc
• Error functions: erf, erfc, erfinv, erfcinv
• Bessel: besselj, bessely, besseli, besselk
• Elliptic integrals: ellipk (complete K), ellipe (complete E), ellipf (incomplete F)
• Airy: airy_ai, airy_bi
• Hypergeometric: hyp1f1, hyp2f1
• Orthogonal polynomials: legendre_p, legendre_plm, hermite_h, laguerre_l, chebyshev_t
• Zeta: zeta, hurwitz_zeta
• Miscellaneous: dawson, fresnel_c, fresnel_s, mittag_leffler, mittag_leffler_1

Composes with

• numra-stats — gamma, beta, erf inside continuous-distribution PDFs and CDFs (direct dependency)
• numra-fde — shares the Mittag-Leffler function family; the two crates ship independent implementations with different signatures, useful for cross-checking
• numra-integrate — special-function integrands appearing in quadrature applications

Install

[dependencies]
numra-special = "0.1"

Or via the umbrella crate:

[dependencies]
numra = "0.1"

Documentation

• API: https://docs.rs/numra-special
• Book: Special functions
• Source: https://github.com/moussaoutlook/numra-rs/tree/main/numra-special

License

Numra Academic & Research License (Non-Commercial). Academic and research use is free; commercial use requires a separate license — contact contact@spectralautomata.com. See LICENSE.