Geodesic
Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems
Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 467-476

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DOI

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.
DOI : 10.4153/CMB-1988-068-6
Mots-clés : 33A65, 33A70 
Rahman, Mizan. Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems. Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 467-476. doi: 10.4153/CMB-1988-068-6
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     title = {Some {Extensions} of {Askey-Wilson's} {Q-Beta} {Integral} and the {Corresponding} {Orthogonal} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {467--476},
     year = {1988},
     volume = {31},
     number = {4},
     doi = {10.4153/CMB-1988-068-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-068-6/}
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