specfun - Special Function Library for Complex Plane Computations

This document introduces a set of specialized mathematical function routines that maintain numerical validity throughout the complete complex plane. The collection encompasses critical functions including: Gamma function (computing factorial values for complex numbers), loggamma function (logarithmic implementation of Gamma for improved numerical stability), psi function (digamma function for logarithmic derivative calculations), polygamma function (higher-order derivatives of the logarithm of Gamma function), error function (Gauss error function for probability integrals), and zeta function (Riemann zeta function for number theory applications). These functions represent fundamental mathematical concepts essential for solving advanced mathematical problems. Through optimized algorithmic implementations featuring Lanczos approximation for Gamma functions, recursive relations for polygamma functions, and convergent series expansions for zeta functions, these routines enable researchers to accurately handle complex mathematical challenges. The code architecture employs rigorous error handling and precision control mechanisms to ensure reliable computations across diverse input domains. Understanding the mathematical definitions and computational implementations of these functions is crucial for effective application in scientific computing and numerical analysis.