Some families of combinatorial and other series identities and their applications

The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox–Wright function p Ψ q and various related generalized hypergeometric functi...

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Vydané v:	Applied mathematics and computation Ročník 218; číslo 3; s. 1077 - 1083
Hlavný autor:	Srivastava, Rekha
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.10.2011
Predmet:	Binomial coefficients and Gamma function Combinatorial analysis Combinatorial series identities and summation formulas Combinatorial series relationships Computation Fox–Wright function pΨq or [formula omitted] and generalized hypergeometric function pFq Higher-order hypergeometric series Hypergeometric functions Joints Karlsson-minton summation formula Mathematical analysis Mathematical models Pfaff–Saalschütz theorem and Euler’s transformation Sums Theorems Vandermonde convolution theorem Binomial coefficients and Gamma function Vandermonde convolution theorem Karlsson-minton summation formula Combinatorial series relationships Fox–Wright function p Ψ q or p Ψ q ∗ and generalized hypergeometric function pF q Pfaff–Saalschütz theorem and Euler’s transformation Combinatorial series identities and summation formulas Higher-order hypergeometric series
ISSN:	0096-3003, 1873-5649
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Popis
Shrnutí:	The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox–Wright function p Ψ q and various related generalized hypergeometric functions. At least one of the hypergeometric summation formulas, which is derived here in this manner, has already found a remarkable application in producing several interesting generalizations of the Karlsson–Minton summation formula. We also consider a number of other combinatorial series identities and rational sums which were proven, in recent works, by using different methods and techniques. We show that much more general results can be derived by means of certain summation theorems for hypergeometric series. Relevant connections of the results presented here with those in the aforementioned investigations are also considered.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2010.12.051