Results 31 to 40 of about 17,253 (231)
Legendre inversions and Ultra-hypergeometric series identities [PDF]
, 2019 In this paper, we extension of hypergeometric series to obtain a new α-hypergeometric series, we establish three terminating Ultra-hypergeometric series identities, by means of Legendre inverse series relations.
Basen +3 more
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Some Summation Theorems for Generalized Hypergeometric Functions
Axioms, 2018 Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized
Mohammad Masjed-Jamei, Wolfram Koepf
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On the parametric behavior of $A$-hypergeometric series
Transactions of the American Mathematical Society, 2017 20 pages; minor ...
Berkesch, Christine +2 more
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Certain Properties Associated with Generalized $M$-Series using Hadamard Product [PDF]
Sahand Communications in Mathematical AnalysisThe generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function. The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and ...
Dheerandra Sachan +2 more
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Summation formulae for elliptic hypergeometric series [PDF]
, 2005 Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well ...
Warnaar, S. O.
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Infinite families of accelerated series for some classical constants by the Markov-WZ Method [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 In this article we show the Markov-WZ Method in action as it finds rapidly converging series representations for a given hypergeometric series. We demonstrate the method by finding new representations for log(2),ζ (2) and ζ (3).
Mohamud Mohammed
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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Abel's method on summation by parts and theta hypergeometric series [PDF]
, 2008 Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established.
JIA C., Chu, Wenchang, Jia, Cangzhi
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Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients
Journal of Function Spaces, 2022 The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into ...
B. R. Srivatsa Kumar +2 more
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