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Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems

Published online by Cambridge University Press:  20 November 2018

Mizan Rahman
Mizan Rahman*
Affiliation:
Department of Mathematics and Statistics, Carleton UniversityOttawa, Ontario K1S 5B6, Canada
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Abstract

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A seven-parameter extension of Askey and Wilson's four parameter q-beta integral is written in a symmetric form as the sum of multiples of two very-well-poised balanced basic hypergeometric 10Φ9 series. Two special cases are considered in which the evaluation of the integral gives single terms by the q-Dixon formula in one case and by a special case of the Verma-Jain formula in the other. An orthogonal polynomial system is obtained in the first case and a system of biorthogonal rational function is obtained in the second. It is also shown that the biorthogonal system represents a generalization of Rogers’ q-ultraspherical polynomials.

Keywords

33A6533A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 467 - 476
Copyright
Copyright © Canadian Mathematical Society 1988

References

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