special-functions-library

# 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