2019/04/24 by Dmitrii Karp, Karp, Dmitrii
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Advanced Mathematical Identities #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1904.10651
In our previous works we found a power series expansion of a particular case of Fox's H function Hq,0p,q in a neighborhood of its positive singularity. An inverse factorial series expansion of the integrand of Hq,0p,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.