General (acm G.1.0), Interpolation (acm G.1.1), Approximation (acm G.1.2), Quadrature and Numerical Differentiation (acm G.1.4), Roots of Nonlinear Equations (acm G.1.5), Ordinary Differential Equations (acm G.1.7)
Research exposition (monographs, survey articles) (msc 33-02), Classical hypergeometric functions, ${}_2F_1$ (msc 33C05), Bessel and Airy functions, cylinder functions, ${}_0F_1$ (msc 33C10), Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ (msc 33C15), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (msc 33C45), Numerical approximation and evaluation (msc 33F05), Approximation by polynomials (msc 41A10), Approximate quadratures (msc 41A55), Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (msc 41A58), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Research exposition (monographs, survey articles) (msc 65-02), Explicit machine computation and programs (not the theory of computation or programming) (msc 65-04), Summation of series (msc 65B10), Euler-Maclaurin formula (msc 65B15), Algorithms for functional approximation (msc 65D15), Computation of special functions, construction of tables (msc 65D20), Numerical integration (msc 65D30), Single equations (msc 65H05)
SIAM
978-0-898716-34

Gil, A, Segura, J, & Temme, N.M. (2007). Numerical Methods for Special Functions. SIAM.