Symbolic Transformations in the Problem of Analytic Continuation of the Hypergeometric FunctionpFp– 1(z) to the Neighborhood of the Point z = 1 in the Logarithmic Case

Abstract

A method of analytic continuation of the generalized hypergeometric function pFp – 1(a; b; z), p > 2, to the neighborhood of the singular point z e 1 in the logarithmic case is developed. The singular component of the function is obtained in an explicit form by means of asymptotic methods and efficient symbolic transformations, and the regular part is found with the help of the finite element and collocation methods.