A note on Fox's H function in the light of Braaksma's results
Abstract
In our previous works we found a power series expansion of a particular case of Fox's $H$ function $H^{q,0}_{p,q}$ in a neighborhood of its positive singularity. An inverse factorial series expansion of the integrand of $H^{q,0}_{p,q}$ served as our main tool. However, a necessary restriction on parameters is missing in those works. In this note we fill this gap and give a simpler and shorter proof of the expansion around the positive singular point. We further identify more precisely the abscissa of convergence of the underlying inverse factorial series. Our new proof hinges on a slight generalization of a particular case of Braaksma's theorem about analytic continuation of Fox's $H$ function.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.10651
 Bibcode:
 2019arXiv190410651K
 Keywords:

 Mathematics  Complex Variables;
 33C60;
 33B15;
 30B50;
 11B68
 EPrint:
 12 pages