Some multiple series identities and their hypergeometric forms (original) (raw)
Related papers
Applications of Some Hypergeometric Summation Theorems Involving Double Series
Journal of Applied Mathematics, Statistics and Informatics, 2012
The main object of this paper is to derive a number of general double series identities and to apply each of these identities in order to deduce several hypergeometric reduction formulas for the Srivastava-Daoust double hypergeometric function. The results presented in this paper are based essentially upon some
Generalized hypergeometric identities with extra parameters
Filomat, 2020
Anew class of hypergeometric identities with extra parameters is introduced in order to generate various kinds of summation theorems for generalized hypergeometric series. Some interesting examples are also given in this direction.
Fractal and Fractional
In this paper, by introducing two sequences of new numbers and their derivatives, which are closely related to the Stirling numbers of the first kind, and choosing to employ six known generalized Kummer’s summation formulas for 2F1(−1) and 2F1(1/2), we establish six classes of generalized summation formulas for p+2Fp+1 with arguments −1 and 1/2 for any positive integer p. Next, by differentiating both sides of six chosen formulas presented here with respect to a specific parameter, among numerous ones, we demonstrate six identities in connection with finite sums of 4F3(−1) and 4F3(1/2). Further, we choose to give simple particular identities of some formulas presented here. We conclude this paper by highlighting a potential use of the newly presented numbers and posing some problems.
Applications of hypergeometric summation theorems of kummer and dixon involving double series
Acta Mathematica Scientia, 2014
Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.
Some applications of a hypergeometric identity
Mathematical Sciences, 2015
In this paper, we use a general identity for generalized hypergeometric series to obtain some new applications. The first application is a hypergeometric-type decomposition formula for elementary special functions and the second one is a generalization of the well-known Euler identity e i x ¼ cos x þ i sin x and an extension of hyperbolic functions in the sequel. Applying the mentioned identity on classical hypergeometric orthogonal polynomials and deriving summation formulae for some classical summation theorems are two further applications of this identity.
Certain Transformations and Summations of Basic Hypergeometric Series
In the present work we have established some new transformations and summations of basic hypergeometric series by making the use of WP-Bailey pairs. Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating is99 transformation. From this result, we deduce new multivariable terminating 1049 transformations, s& summations and other identities. We also use similar methods to derive new multivariable r+t summations. Some of our results are extended to the case of elliptic hypergeometric series.
Hypergeometric series and harmonic number identities
Advances in Applied Mathematics, 2005
The classical hypergeometric summation theorems are exploited to derive several striking identities on harmonic numbers including those discovered recently by Paule and Schneider (2003).
Some expansions of hypergeometric functions in series of hypergeometric functions†
Glasgow Mathematical Journal, 1976
Throughout the present note we abbreviate the set of p parameters a1,…,ap by (ap), with similar interpretations for (bq), etc. Also, by [(ap)]m we mean the product , where [λ]m = Г(λ + m)/ Г(λ), and so on. One of the main results we give here is the expansion formula(1)which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative integers such that p+r < q+s+l (or p+r = q+s+l and |zω| <1), p+t < q+u (or p + t = q + u and |z| < 1), and the various parameters including μ are so restricted that each side of equation (1) has a meaning.