Successive derivatives of Whittaker functions with respect to the first parameter Original Research Article

Algorithms are given for the computation of the nth derivatives of the Whittaker functions Mκ,μ(z) and Wκ,μ(z) with respect to the parameter κ. The algorithms are based on a convergent expansion, due to Buchholz, of Mκ,μ(z) in series of Bessel functions. Properties of the Buchholz polynomials and algorithms for evaluating the n-derivative of the reciprocal Gamma function are discussed in two appendices.