## Rocky Mountain Journal of Mathematics

### An Extension of Askey-Wilson's $q$-Beta Integral and Its Applications

#### Article information

Source
Rocky Mountain J. Math., Volume 22, Number 2 (1992), 733-756.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181072764

Digital Object Identifier
doi:10.1216/rmjm/1181072764

Mathematical Reviews number (MathSciNet)
MR1180735

Zentralblatt MATH identifier
0760.33010

#### Citation

Verma, A.; Jain, V.K. An Extension of Askey-Wilson's $q$-Beta Integral and Its Applications. Rocky Mountain J. Math. 22 (1992), no. 2, 733--756. doi:10.1216/rmjm/1181072764. https://projecteuclid.org/euclid.rmjm/1181072764

#### References

• R.P. Agarwal, Some transformations of well-poised basic hypergeometric series of the type $_8\phi_7$, Proc. Amer. Math. Soc. 4 (1953), 678-685.
• W.A. Al Salam and A. Verma, Some remarks on $q$-beta integral, Proc. Amer. Math. Soc. 85 (1982), 360-362.
• R. Askey and J.A. Wilson, Some basic hypergeometric polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985).
• W.N. Bailey, Generalized hypergeometric series, Stechert-Hafner Service Agency, New York and London, 1964.
• M.E.H. Ismail, D. Stanton and G. Viennot, The combinatorics of $q$-Hermite polynomials and the Askey-Wilson integral, European J. Combinatorics 8 (1987), 379-392.
• B. Nassrallah and Mizan Rahman, Projection formulas, a reproducing kernel and a generating function for $q$-Wilson polynomials, SIAM J. Math. Anal. 16 (1985), 186-197.
• --------, A $q$-analogue of Appell's $F_1$ function and some quadratic transformation formulas for nonterminating basic hypergeometric series, Rocky Mountain J. Math. 16 (1986), 63-82.
• A. Verma and V.K. Jain, Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type, J. Math. Anal. Appl. 76 (1980), 230-269.
• --------, Transformations of nonterminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identities, J. Math. Anal. Appl. 87 (1982), 9-44.