An Inverse Factorial Series for a General Gamma Ratio and Related Properties of the Nørlund–Bernoulli Polynomials
- Авторлар: Karp D.1, Prilepkina E.1
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Мекемелер:
- Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
- Шығарылым: Том 234, № 5 (2018)
- Беттер: 680-696
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241977
- DOI: https://doi.org/10.1007/s10958-018-4036-1
- ID: 241977
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
D. Karp
Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
Хат алмасуға жауапты Автор.
Email: dimkrp@gmail.com
Ресей, Vladivostok
E. Prilepkina
Far Eastern Federal University and Institute of Applied Mathematics of the FEBRAS
Email: dimkrp@gmail.com
Ресей, Vladivostok