An Inverse Factorial Series for a General Gamma Ratio and Related Properties of the Nørlund–Bernoulli Polynomials
- Authors: Karp D.B.1, Prilepkina E.G.1
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Affiliations:
- Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
- Issue: Vol 234, No 5 (2018)
- Pages: 680-696
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241977
- DOI: https://doi.org/10.1007/s10958-018-4036-1
- ID: 241977
Cite item
Abstract
The inverse factorial series expansion for the ratio of products of gamma functions whose arguments are linear functions of the variable is found. A recurrence relation for the coefficients in terms of the Nørlund–Bernoulli polynomials is provided, and the half-plane of convergence is determined. The results obtained naturally supplement a number of previous investigations of the gamma ratios, which began in the 1930-ies. The expansion obtained in this paper plays a crucial role in the study of the behavior of the delta-neutral Fox’s H-function in the neighborhood of its finite singular point. A particular case of the inverse factorial series expansion is used in deriving a possibly new identity for the Nørlund–Bernoulli polynomials.
About the authors
D. B. Karp
Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
Author for correspondence.
Email: dimkrp@gmail.com
Russian Federation, Vladivostok
E. G. Prilepkina
Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
Email: dimkrp@gmail.com
Russian Federation, Vladivostok