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On another extension of \(q\)-Pfaff-Saalschütz formula. (English) Zbl 1224.05037

Summary: We give an extension of \(q\)-Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of \(q\)-Chu-Vandermonde convolution formula and some other \(q\)-identities.

MSC:

05A30 \(q\)-calculus and related topics
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals
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References:

[1] G. E. Andrews and R. Askey: Another q-extension of the beta function. Proc. Amer. Math. Soc. 81 (1981), 97–100. · Zbl 0471.33001
[2] G. E. Andrews: q-Series: Their Development and Applications in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra. CBMS Regional Conference Lecture Series, vol. 66, Amer. Math, Providences, RI, 1986.
[3] F. H. Jackson: On q-definite integrals. Quart. J. Pure and Appl. Math. 41 (1910), 193–203.
[4] M. Wang: A remark on Andrews-Askey integral. J. Math. Anal. Appl. 341/2 (2008), 14870–1494. · Zbl 1142.33006 · doi:10.1016/j.jmaa.2007.11.011
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