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special-functions-library

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Comprehensive special functions evaluation and manipulation

General

What this skill does


# 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

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