On the hfunction
Abstract
The paper is devoted to study the $H$function defined by the MellinBarnes integral $$H^{m,n}_{\thinspace p,q}(z)={\frac1{2\pi i}}\int_{\Lss} \HHs^{m,n}_{\thinspace p,q}(s)z^{s}ds,$$ where the function $\HH^{m,n}_{\thinspace p,q}(s)$ is a certain ratio of products of Gamma functions with the argument $s$ and the contour $\LL$ is specially chosen. The conditions for the existence of $H^{m,n}_{\thinspace p,q}(z)$ are discussed and explicit power and powerlogarithmic series expansions of $H^{m,n}_{p,q}(z)$ near zero and infinity are given. The obtained results define more precisely the known results.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 1998
 DOI:
 10.48550/arXiv.math/9803163
 arXiv:
 arXiv:math/9803163
 Bibcode:
 1998math......3163K
 Keywords:

 Mathematics  Classical Analysis and ODEs