Reduction of hypergeometric functions with integral parameter differences

Karlsson, Per W.

doi:10.1016/1385-7258(74)90035-3

Cited by 7 publications

(15 citation statements)

References 2 publications

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“…Our summation formulas (31) and (32) match very well the recent trend of finding new relationships for generalized hypergeometric functions. In fact, they are immediate and natural generalizations of more special formulas suggested, a decade ago, by Milgram [8,9,10,11], which were further proved and employed by Miller and Paris [12] and Rathie and Paris [13] quite recently.…”

Section: Introductionsupporting

confidence: 80%

“…In 1974, Karlsson [31] derived a quite general reduction formula for generalized hypergeometric functions p F q (z) with generic negative integral parameter differences and for p ≦ q + 1. In the case when p = q + 1 = 3, his equation ( 6) in [31] may be written as follows:…”

Section: Background Resultsmentioning

confidence: 99%

“…The main object of the present paper is to derive two elegant and manifestly symmetric summation formulas (31) and (32) for Clausen's series 3 F 2 with unit argument (see, e.g., [1,2,3,4,5,6,7])…”

Section: Introductionmentioning

confidence: 99%

“…In the following section, we explicitly write down the previous results of [31], [8,11] and [12], which will be needed for establishing the necessary contacts and connections with the present work.…”

Section: Introductionmentioning

confidence: 99%

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The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

Shpot,

Srivastava

2014

Preprint

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New explicit as well as manifestly symmetric three-term summation formulas are derived for the Clausenian hypergeometric series 3 F 2 (1) with negative integral parameter differences. Our results generalize and naturally extend several similar relations published, in recent years, by many authors. An appropriate and useful connection is established with the quite underestimated 1974 paper by P. W. Karlsson.

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Section: Introductionsupporting

confidence: 80%

Section: Background Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

Shpot,

Srivastava

2014

Preprint

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“…(iii) The method in (ii) is to obtain summation formulas for certain generalized hypergeometric functions of higher order from those of lower order. Conversely, reduction formulas of generalized hypergeometric and their extended special functions are to reduce those of higher order to some other ones of lower order (see, e.g., [14,[38][39][40][41][42][43][44][45]).…”

Section: Introductionmentioning

confidence: 99%

Reduction Formulas for Generalized Hypergeometric Series Associated with New Sequences and Applications

et al. 2021

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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.

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Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I. Connection to the hypergeometric function $$_{3}{{\varvec{F}}}_{2}$$

2016

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Reduction of hypergeometric functions with integral parameter differences

Cited by 7 publications

References 2 publications

The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

Reduction Formulas for Generalized Hypergeometric Series Associated with New Sequences and Applications

Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I. Connection to the hypergeometric function $$_{3}{{\varvec{F}}}_{2}$$

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