  Hypergeometric structures in single and multiscale Feynman integrals emerge
in a wide class of topologies. Using integration-by-parts relations, associated
master or scalar integrals have to be calculated. For this purpose it appears
useful to devise an automated method which recognizes the respective (partial)
differential equations related to the corresponding higher transcendental
functions. We solve these equations through associated recursions of the
expansion coefficient of the multivalued formal Taylor series. The expansion
coefficients can be determined using either the package {\tt Sigma} in the case
of linear difference equations or by applying heuristic methods in the case of
partial linear difference equations. In the present context a new type of sums
occurs, the Hurwitz harmonic sums, and generalized versions of them. The code
{\tt HypSeries} transforming classes of differential equations into analytic
series expansions is described. Also partial difference equations having
rational solutions and rational function solutions of Pochhammer symbols are
considered, for which the code {\tt solvePartialLDE} is designed. Generalized
hypergeometric functions, Appell-,~Kamp\'e de F\'eriet-, Horn-,
Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We
illustrate the algorithms by examples.
