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Journal of Difference Equations and Applications Volume 17, 2011 - Issue 10
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Original Articles

An extension of the non-terminating 6φ5 summation and the Askey–Wilson polynomials

Zhi-Guo Liu Department of Mathematics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, P.R. ChinaCorrespondence[email protected] [email protected]
Pages 1401-1411 | Received 06 Mar 2009, Accepted 03 Dec 2009, Published online: 24 Feb 2010

Citations (37)

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Sama Arjika. (2020) q-difference equations for homogeneous q-difference operators and their applications. Journal of Difference Equations and Applications 26:7, pages 987-999.
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Xue-Fang Wang & Jian Cao. (2018) q-Difference equations for the generalized Cigler’s polynomials. Journal of Difference Equations and Applications 24:4, pages 479-502.
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Da-Wei Niu & Long Li. (2018) q-Laguerre polynomials and related q-partial differential equations. Journal of Difference Equations and Applications 24:3, pages 375-390.
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Jian Cao & Da-Wei Niu. (2016) A note on q-difference equations for Cigler’s polynomials. Journal of Difference Equations and Applications 22:12, pages 1880-1892.
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Jian-Ping Fang. (2015) Remarks on a generalized q-difference equation. Journal of Difference Equations and Applications 21:10, pages 934-953.
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Jian Cao & Tianxin Cai. (2014) q-Difference equations of moment integrals for transformational identities and generating functions. Journal of Difference Equations and Applications 20:12, pages 1592-1608.
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Jian Cao. (2014) q-Difference equations for generalized homogeneous q-operators and certain generating functions. Journal of Difference Equations and Applications 20:5-6, pages 837-851.
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Articles from other publishers (30)

Bing He & Suzhen Wen. (2023) Multiple Expansion Formulas over Root Systems. Results in Mathematics 79:1.
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Zhi Guo Liu. (2023) A Multiple q-translation Formula and Its Implications. Acta Mathematica Sinica, English Series 39:12, pages 2338-2363.
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Zhiguo Liu. (2023) A multiple q-exponential differential operational identity. Acta Mathematica Scientia 43:6, pages 2449-2470.
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Zhiguo Liu. (2023) A q-operational equation and the Rogers-Szegő polynomials. Science China Mathematics 66:6, pages 1199-1216.
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Dunkun Yang. (2022) An expansion of $$(q, \lambda )$$-derivative operator. The Ramanujan Journal 60:4, pages 1127-1149.
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Jian Cao, Jin-Yan Huang, Mohammed Fadel & Sama Arjika. (2023) A Review of q-Difference Equations for Al-Salam–Carlitz Polynomials and Applications to U(n + 1) Type Generating Functions and Ramanujan’s Integrals. Mathematics 11:7, pages 1655.
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Ying Zhang & Wenlong Zhang. (2021) Hecke–Rogers type series representations for infinite products. The Ramanujan Journal 58:3, pages 889-903.
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Jian Cao, Binbin Xu & Sama Arjika. (2020) A note on generalized q-difference equations for general Al-Salam–Carlitz polynomials. Advances in Difference Equations 2020:1.
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Hari M. Srivastava, Jian Cao & Sama Arjika. (2020) A Note on Generalized q-Difference Equations and Their Applications Involving q-Hypergeometric Functions. Symmetry 12:11, pages 1816.
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Helen W.J. Zhang. (2020) (q,c)-Derivative operator and its applications. Advances in Applied Mathematics 121, pages 102081.
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Jian Cao. (2018) A note on q-difference equations for Ramanujan’s integrals. The Ramanujan Journal 48:1, pages 63-73.
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Zeya Jia & Jiang Zeng. (2017) Expansions in Askey–Wilson polynomials via Bailey transform. Journal of Mathematical Analysis and Applications 452:2, pages 1082-1100.
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Jian Cao & Da-Wei Niu. (2017) q-difference equations for Askey–Wilson type integrals via q-polynomials. Journal of Mathematical Analysis and Applications 452:2, pages 830-845.
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Jian Cao. (2017) Homogeneous q-partial difference equations and some applications. Advances in Applied Mathematics 84, pages 47-72.
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Zhi-Guo Liu. 2017. Analytic Number Theory, Modular Forms and q-Hypergeometric Series. Analytic Number Theory, Modular Forms and q-Hypergeometric Series 445 461 .
Zhi-Guo Liu. (2016) On a Reduction Formula for a Kind of Double q-Integrals. Symmetry 8:6, pages 44.
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Mourad E.H. Ismail & Plamen Simeonov. (2016) Formulas and identities involving the Askey–Wilson operator. Advances in Applied Mathematics 76, pages 68-96.
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Jian Cao. (2015) Homogeneous $$q$$ q -difference equations and generating functions for $$q$$ q -hypergeometric polynomials. The Ramanujan Journal 40:1, pages 177-192.
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Zhi-Guo Liu & Jiang Zeng. (2015) Two expansion formulas involving the Rogers–Szegő polynomials with applications. International Journal of Number Theory 11:02, pages 507-525.
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Jian-Ping Fang. (2014) Applications of a generalized q-difference equation. Advances in Difference Equations 2014:1.
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Jian-Ping Fang. (2014) q-Difference equation and q-polynomials. Applied Mathematics and Computation 248, pages 550-561.
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Zhi-Guo Liu. (2014) A q-summation formula, the continuous q-Hahn polynomials and the big q-Jacobi polynomials. Journal of Mathematical Analysis and Applications 419:2, pages 1045-1064.
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Jian Cao. (2014) A note on generalized q -difference equations for q -beta and Andrews–Askey integral. Journal of Mathematical Analysis and Applications 412:2, pages 841-851.
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Jian Cao. (2014) A note on moment integrals and some applications. Journal of Mathematical Analysis and Applications 410:1, pages 348-360.
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Jian Cao. (2013) A Note on q -Integrals and Certain Generating Functions . Studies in Applied Mathematics 131:2, pages 105-118.
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Jian Cao & H.M. Srivastava. (2013) Some q-generating functions of the Carlitz and Srivastava–Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers–Szegö polynomials. Applied Mathematics and Computation 219:15, pages 8398-8406.
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Zhi-Guo Liu. (2012) A q-series expansion formula and the Askey–Wilson polynomials. The Ramanujan Journal 30:2, pages 193-210.
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Jian Cao. (2013) Some Integrals Involving -Laguerre Polynomials and Applications . Abstract and Applied Analysis 2013, pages 1-13.
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Jian Cao. (2012) Generalizations of certain Carlitz’s trilinear and Srivastava–Agarwal type generating functions. Journal of Mathematical Analysis and Applications 396:1, pages 351-362.
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Jian Cao. (2012) Moments for Generating Functions of Al-Salam-Carlitz Polynomials. Abstract and Applied Analysis 2012, pages 1-18.
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