Journal of Mathematical Sciences

, Volume 234, Issue 5, pp 680–696 | Cite as

An Inverse Factorial Series for a General Gamma Ratio and Related Properties of the Nørlund–Bernoulli Polynomials

  • D. B. KarpEmail author
  • E. G. Prilepkina

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.


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Authors and Affiliations

  1. 1.Far Eastern Federal University and Institute of Applied Mathematics of the FEBRASVladivostokRussia

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