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Keywords:
Andrews-Askey integral; $_{r+1}\phi _r$ basic hypergeometric series; $q$-Pfaff-Saalschütz formula; $q$-Chu-Vandermonde convolution formula
Andrews-Askey integral; $_{r+1}\phi _r$ basic hypergeometric series; $q$-Pfaff-Saalschütz formula; $q$-Chu-Vandermonde convolution formula
Summary:
In this paper 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.
References:
[1] Andrews, G. E., Askey, R.: Another $q$-extension of the beta function. Proc. Amer. Math. Soc. 81 (1981), 97-100. MR 0589145 | Zbl 0471.33001
[2] Andrews, G. E.: $q$-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). MR 0858826
[3] Jackson, F. H.: On $q$-definite integrals. Quart. J. Pure and Appl. Math. 41 (1910), 193-203.
[4] Wang, M.: A remark on Andrews-Askey integral. J. Math. Anal. Appl. 341/2 (2008), 14870-1494. DOI 10.1016/j.jmaa.2007.11.011 | MR 2398544 | Zbl 1142.33006
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