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In this paper we extend the two $q$-additions with powers in the umbrae, define a $q$-multinomial-coefficient, which implies a vector version of the $q$-binomial theorem, and an arbitrary complex power of a JHC power series is shown to be equivalent to a special case of the first $q$-Lauricella function. We then present several $q$-analogues of hypergeometric integral formulas from the two books by Exton and the paper by Choi and Rathie. We also find multiple $q$-analogues of hypergeometric integral formulas from the recent paper by Kim. Finally, we prove several multiple $q$-hypergeometric integral formulas emanating from a paper by Koschmieder, which are special cases of more general formulas by Exton.
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참고문헌 (13)
참고문헌 신청
J. Choi / 2015 / Evaluation of certain new class of definite integrals / Integral Transforms Spec. Funct. 26(4):282~294
T. Ernst / 2011 / Multiple q-hypergeometric transformations involving q-integrals / Proceedings of the 9th Annual Conference of the Society for Special Functions and their Applications (SSFA) 9:91~99
T. Ernst / 2012 / A Comprehensive Treatment of q-Calculus / Birkhauser
T. Ernst / 2012 / Convergence aspects for q-Lauricella functions I / Advanced Studies in Contemporary Mathematics 22(1):35~50
T. Ernst / 2016 / On the symmetric q-Lauricella functions / Proc. Jangjeon Math. Soc. 19(2):319~344
T. Ernst / 2011 / Multiple q-hypergeometric transformations involving q-integrals / Proceedings of the 9th Annual Conference of the Society for Special Functions and their Applications (SSFA) 9:91~99
T. Ernst / 2012 / A Comprehensive Treatment of q-Calculus / Birkhauser
T. Ernst / 2012 / Convergence aspects for q-Lauricella functions I / Advanced Studies in Contemporary Mathematics 22(1):35~50
T. Ernst / 2016 / On the symmetric q-Lauricella functions / Proc. Jangjeon Math. Soc. 19(2):319~344
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