On theH-function

[摘要] This paper is devoted to the study of theH-function as defined by the Mellin-Barnes integralHp,qm,n(z)=12πi∫ℒℋp,qm,n(s)z−sds,where the functionℋp,qm,n(s)is a certain ratio of products of the Gamma-functions with the argumentsand the contourℒspecially chosen. The conditions for the existence ofHp,qm,n(z)are discussed and explicit power and power-logarithmic series expansions ofHp,qm,n(z)near zero and infinity are given. The obtained results define more precisely the known results.

[学科分类] 应用数学