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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Veröffentlicht in:Applied mathematics and computation Jg. 218; H. 3; S. 1077 - 1083
1. Verfasser: Srivastava, Rekha
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.10.2011
Schlagworte:
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
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.12.051