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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Some remarks on $q$-beta integral


Authors: W. A. Al-Salam and A. Verma
Journal: Proc. Amer. Math. Soc. 85 (1982), 360-362
MSC: Primary 33A15; Secondary 33A65
DOI: https://doi.org/10.1090/S0002-9939-1982-0656102-7
MathSciNet review: 656102
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Abstract: The following $q$-integral \[ \int _{ - c}^d {\frac {{{{( - qt/c)}_{\alpha - 1}}{{(qt/d)}_{\beta - 1}}}} {{{{( - qet)}_{\alpha + \beta }}}}} {d_q}t\] is evaluated. A more general $q$-integral is also considered. Some applications to the $q$-Wilson (or Askey-Wilson) polynomials are also given.


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Keywords: <IMG WIDTH="15" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$q$">-beta integrals, Askey-Wilson polynomials, basic series
Article copyright: © Copyright 1982 American Mathematical Society