Some remarks on $q$-beta integral
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- by W. A. Al-Salam and A. Verma
- Proc. Amer. Math. Soc. 85 (1982), 360-362
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656102-7
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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.References
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- Alexander Dinghas, Zur Darstellung einiger Klassen hypergeometrischer Polynome durch Integrale vom Dirichlet-Mehlerschen Typus, Math. Z. 53 (1950), 76ā€“83 (German). MR 36876, DOI 10.1007/BF01175582
- D. B. Sears, Transformations of basic hypergeometric functions of special type, Proc. London Math. Soc. (2) 52 (1951), 467ā€“483. MR 41982, DOI 10.1112/plms/s2-52.6.467
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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