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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
Asena Çetinkayaa, Dmitrii Karpbc, Elena Prilepkinacd a İstanbul Kultur University, İstanbul, Turkey
b Holon Institute of Technology, Holon, Israel
c Far Eastern Federal University, Ajax Bay 10, Vladivostok, 690922, Russia
d Institute of Applied Mathematics, FEBRAS, 7 Radio Street, Vladivostok, 690041, Russia
Аннотация:
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of Meijer's $G$ function. For instance, we recover two- and three-term Thomae relations for ${}_3F_2$, give two- and three-term transformations for ${}_4F_3$ with one unit shift and ${}_5F_4$ with two unit shifts in the parameters, establish multi-term identities for general ${}_{p}F_{p-1}$ and several transformations for terminating Kampé de Fériet and Srivastava $F^{(3)}$ functions. We further present a presumably new formula for analytic continuation of ${}_pF_{p-1}(1)$ in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and $q$-hypergeometric functions to derive multi-term relations for terminating series.
Ключевые слова:
generalized hypergeometric function, Meijer's $G$ function, multiple hypergeometric series, Kampé de Fériet function, Srivastava function, hypergeometric identity, generalized Bernoulli polynomials.
Поступила: 20 мая 2021 г.; в окончательном варианте 31 октября 2021 г.; опубликована 7 ноября 2021 г.
Образец цитирования:
Asena Çetinkaya, Dmitrii Karp, Elena Prilepkina, “Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities”, SIGMA, 17 (2021), 098, 25 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1780 https://www.mathnet.ru/rus/sigma/v17/p98
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