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
- Function Selection: Choose appropriate function definitions
- Numerical Evaluation: Use high-precision arithmetic when needed
- Identities: Apply transformation and connection formulas
- Asymptotics: Use asymptotic expansions for large arguments
Tools/Libraries
- DLMF (Digital Library of Mathematical Functions)
- mpmath
- scipy.special