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Focusing on special functions in both real and complex domains, this handbook provides insights into over 170 functions essential for physics applications. It includes MATLAB-based programs and comprehensive documentation to aid efficient computation. Key functions featured are the Gamma and Beta functions, Legendre functions, Bessel functions, hypergeometric functions, orthogonal polynomials, and Riemann zeta functions, all crucial in fields like quantum mechanics and mathematical physics. Targeted at scientists, researchers, and advanced students, it serves as a valuable resource for practical applications in physics and engineering.