Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker WIκ,μ/I Function II

In the first part of this investigation, we considered the parameter differentiation of the Whittaker function M[sub.κ,μ] (x). In this second part, first derivatives with respect to the parameters of the Whittaker function W[sub.κ,μ] (x) are calculated. Using the confluent hypergeometric function, these derivatives can be expressed as infinite sums of quotients of the digamma and gamma functions. Furthermore, it is possible to obtain these parameter derivatives in terms of infinite integrals, with integrands containing elementary functions (products of algebraic, exponential, and logarithmic functions), from the integral representation of W[sub.κ,μ] (x). These infinite sums and integrals can be expressed in closed form for particular values of the parameters. Finally, an integral representation of the integral Whittaker function wi[sub.κ,μ] (x) and its derivative with respect to κ, as well as some reduction formulas for the integral Whittaker functions Wi[sub.κ,μ] (x) and wi[sub.κ,μ] (x), are calculated.