Search Results - summation formulas for generalized hypergeometric functions

On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas by González-Santander, Juan Luis

“…We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas…”
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On Two Summation Formulas for the Generalized Hypergeometric Functions 3F2(1) and 4F3(1) by Atash, Ahmed Ali, Bellehaj, Hussein Saleh

“…In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1…”
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Generalized harmonic number summation formulae via hypergeometric series and digamma functions by Liu, Hongmei, Zhou, Wenshu, Ding, Shuyan

“…By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae…”
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Three General Double-Series Identities and Associated Reduction Formulas and Fractional Calculus by Qureshi, Mohd Idris, Shah, Tafaz Ul Rahman, Choi, Junesang, Bhat, Aarif Hussain

“…–D function or KDF function to the generalized hypergeometric function pFq. Additionally, we provide general summation formulas for the pFq and S–D function (or KDF function…”
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Some new summation formulae for the generalised hypergeometric function of higher order by Exton, Harold

“…A consideration of odd and even terms of hypergeometric series of higher order leads to new summation formulae with arguments 1 and −1…”
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On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences by Bakhtin, Kirill, Prilepkina, Elena

“…In this paper, we present an extension of the Karlsson–Minton summation formula for a generalized hypergeometric function with integral parameter differences…”
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Some families of combinatorial and other series identities and their applications by Srivastava, Rekha

“… associated with the Fox–Wright function p Ψ q and various related generalized hypergeometric functions…”
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Extensions of Karlsson-Minton summation theorem and some consequences of the first Miller-Paris transformation by Karp, D. B., Prilepkina, E. G.

“…In this paper, we give several independent extensions of the Karlsson-Minton summation formula for the generalized hypergeometric function with integral parameters differences…”
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Certain Generalizations of Quadratic Transformations of Hypergeometric and Generalized Hypergeometric Functions by Qureshi, Mohd Idris, Choi, Junesang, Shah, Tafaz Rahman

“… Among the various approaches to these functions, the transformation formulae for the hypergeometric series 2F1 and the generalized hypergeometric series pFq are significant, both in terms of applications and theory…”
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Evaluation of certain families of log-cosine integrals using hypergeometric function approach and applications by Qureshi, Mohammad Idris, Malik, Shakir Hussain

“… As applications, we obtain some mixed summation formulas (19), (35) and (46) involving generalized hypergeometric functions $_3F_2,$ $_5F_4$ and $_7F_6…”
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Certain summation formulas involving harmonic numbers and generalized harmonic numbers by Choi, Junesang

“… to a known summation formula for the hypergeometric function 5 F 4(1)…”
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Contribution for the Summation Formulas for the Generalized Hypergeometric Series F65−1 by Jayarama, Prathima, Lim, Dongkyu, Rathie, Arjun Kumar

“…In this paper, our aim is to provide as many as one hundred and ninety-two summation formulas for the generalized hypergeometric series F65…”
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Some Summation Theorems for Generalized Hypergeometric Functions by Masjed-Jamei, Mohammad, Koepf, Wolfram

“…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…”
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Further summation formulae related to generalized harmonic numbers by Zheng, De-Yin

“… More summation formulae have systematically been derived by Chu [W. Chu, Hypergeometric series and the Riemann Zeta function, Acta Arith. 82 (1997) 103–118…”
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A New Identity for Generalized Hypergeometric Functions and Applications by Masjed-Jamei, Mohammad, Koepf, Wolfram

“…We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas…”
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Transformations of well-poised hypergeometric functions over finite fields by McCarthy, Dermot

“…We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series…”
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Infinite summation formulas related to Riemann Zeta function from hypergeometric series by Chen, Yuwu, Wang, Xiaoxia

“…Applying Gauss and Watson's famous hypergeometric summation theorems, the authors establish two pattern infinite summation formulas involving generalized…”
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Contribution for the Summation Formulas for the Generalized Hypergeometric Series 6 F 5 (−1) by Jayarama, Prathima, Lim, Dongkyu, Rathie, Arjun Kumar

“…In this paper, our aim is to provide as many as one hundred and ninety‐two summation formulas for the generalized hypergeometric series 6 F 5 (−1…”
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A study on certain properties of generalized special functions defined by Fox-Wright function by Ata, Enes, Kıymaz, İ. Onur

“… For all the generalized functions we have defined, we obtained their integral representations, summation formulas, transformation formulas, derivative formulas and difference formulas…”
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Summations and transformations for very well-poised hypergeometric functions 2q+5F2q+4(1) and 2q+7F2q+6(1) with arbitrary integral parameter differences by Vyas, Yashoverdhan, Fatawat, Kalpana

“…The present paper aims to derive summation and transformation formulae for the generalized very well-poised hypergeometric functions 2q+5F2q+4(1) and 2q+7F2q+6(1…”
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