Geodesic
A $q$-Analogue of the Euler Gamma Integral
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 20-30

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We discuss $q$-analogues of the Euler reflection formula and the Euler gamma integral. The central role here is played by the Ramanujan $q$-extension of the Euler integral representation for the gamma function, which allows deriving the Mellin integral transformations for the $q$-polynomials of Stieltjes–Wigert, Rogers–Szegö, Laguerre, and Wall, for the alternative $q$-polynomials of Charlier, and for the little $q$-polynomials of Jacobi. 
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     author = {N. M. Atakishiyev and M. K. Atakishiyeva},
     title = {A $q${-Analogue} of the {Euler} {Gamma} {Integral}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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N. M. Atakishiyev; M. K. Atakishiyeva. A $q$-Analogue of the Euler Gamma Integral. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 20-30. http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a2/