Special Functions Library

Purpose

Provides comprehensive capabilities for special functions evaluation, manipulation, and analysis.

Capabilities

• Bessel, hypergeometric, elliptic functions
• Orthogonal polynomials (Legendre, Chebyshev, Hermite)
• Gamma, beta, zeta functions
• Asymptotic expansions
• Connection formulas and identities

Usage Guidelines

1. Function Selection: Choose appropriate function definitions
2. Numerical Evaluation: Use high-precision arithmetic when needed
3. Identities: Apply transformation and connection formulas
4. Asymptotics: Use asymptotic expansions for large arguments

Tools/Libraries

• DLMF (Digital Library of Mathematical Functions)
• mpmath
• scipy.special