Suchergebnisse - summation formulas for generalized hypergeometric functions

On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas von 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) von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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 von 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) von 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 von 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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ON GENERALIZED EXTENDED BETA AND HYPERGEOMETRIC FUNCTIONS von Shoukat Ali, Naresh Kumar Regar, Subrat Parida

“… In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions …”
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