Search Results - Nonterminating basic hypergeometric functions

Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals by Cohl, Howard S., Costas-Santos, Roberto S.

“… We derive some interesting q-Mellin–Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions…”
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Nonterminating transformations and summations associated with some q-Mellin--Barnes integrals by Cohl, Howard S, Costas-Santos, Roberto S

“… We derive some interesting \(q\)-Mellin--Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions…”
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A \(q\)-Chaundy representation for the product of two nonterminating basic hypergeometric series and symmetric and dual relations by Cohl, Howard S, Costas-Santos, Roberto S

“…\)-Chaundy theorem which expresses a product of two nonterminating basic hypergeometric series as a sum over a terminating basic hypergeometric series, we study generating functions for the symmetric…”
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Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials by Cohl, Howard, Schlosser, Michael

“…) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which contains an extra parameter…”
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Two new transformation formulas of basic hypergeometric series by Zhang, Caihuan, Zhang, Zhizheng

“… These contain several important identities for basic hypergeometric series as special cases, including the nonterminating q…”
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Another class of nonterminating F23-series with a free argument by Li, Nadia N., Chu, Wenchang

“…By means of the linearization method, we evaluate another class of nonterminating F 2 3 -series with a free argument x and two perturbing integer parameters m…”
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A symmetric formula for hypergeometric series by Wei, Chuanan

“…In terms of Dougall’s 2 H 2 series identity and the series rearrangement method, we establish a symmetric formula for hypergeometric series…”
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Utility of integral representations for basic hypergeometric functions and orthogonal polynomials by Cohl, Howard S., Costas-Santos, Roberto S.

“…We describe the utility of integral representations for sums of basic hypergeometric functions…”
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Generalizations of a terminating summation formula of basic hypergeometric series and their applications by Zhu, Jun-Ming

“…We generalize a terminating summation formula to a unilateral nonterminating, and further, a bilateral summation formula by a property of analytic functions…”
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Some Summation Formulae for Nonterminating Basic Hypergeometric Series by Verma, A., Jain, V. K.

“…Basic hypergeometric series extensions of some classical results on hypergeometric series are obtaitied…”
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Utility of integral representations for basic hypergeometric functions and orthogonal polynomials by Cohl, Howard S, Costas-Santos, Roberto S

“…We describe the utility of integral representations for sums of basic hypergeometric functions…”
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Summations for basic hypergeometric series involving a q-analogue of the digamma function by Krattenthaler, C., Srivastava, H.M.

“… At the result side of the basic hypergeometric summations, there appears a q-analogue of the digamma function…”
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Bisection Series Approach for Exotic 3F2(1)-Series by Chen, Marta Na, Chu, Wenchang

“…By employing the bisection series approach, two classes of nonterminating 3F2(1)-series are examined…”
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A Nonterminating q -Clausen Formula and Some Related Product Formulas by Gasper, George, Rahman, Mizan

“…$-ultraspherical polynomials and a quadratic transformation formula for well-poised basic hypergeometric _2 \phi _1…”
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The Saalschütz chain reactions and bilateral basic hypergeometric series by Chu, Wenchang

“…]. These transformations further yield a number of closed formulas of very well-poised bilateral basic hypergeometric series…”
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Generalizations of a terminating summation formula of basic hypergeometric series and their applications by Jun-Ming, Zhu

“…We generalize a terminating summation formula to a unilateral nonterminating, and further, a bilateral summation formula by a property of analytic functions…”
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Basic bilateral very well-poised series and Shukla's 8ψ8-summation formula by WENCHANG CHU, XIAOXIA WANG

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The q -WZ method for infinite series by Chen, William Y.C., Xia, Ernest X.W.

“… in the approach of Chen, Hou and Mu to prove nonterminating basic hypergeometric series identities…”
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A unified approach to the summation and integration formulas for q-hypergeometric functions I by Rahman, Mizan, Suslov, SergeĭK.

“…The most basic summation formula in the theory of q-hypergeometric functions is the well-known q-binomial formula…”
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Positivity of the Poisson Kernel for the Continuous q -Jacobi Polynomials and Some Quadratic Transformation Formulas for Basic Hypergeometric Series by Gasper, George, Rahman, Mizan

“…A nonterminating extension of the Sears-Carlitz quadratic transformation formula for a well-posed _3 \phi _2…”
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