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TMF, 1995, Volume 105, Number 3, Pages 383–392 (Mi tmf1382)  

Ramanujan-type continuous measures for classical $q$-polynomials

N. M. Atakishiyevab

a Institute of Physics Azerbaijan Academy of Sciences
b National Autonomous University of Mexico, Institute of Mathematics

Abstract: It is shown that Ramanujan-type measures for a hierarchy of classical $q$-orthogonal polynomials can be systematically built from simple cases of the continuous $q$-Hermite and $q^{-1}$-Hermite polynomials by using the Berg–Ismail procedure of attaching generating functions to measures. The application of this technique leads also to the evaluation of Ramanujan-type integrals for the Al-Salam–Chihara polynomials both when $0<q<1$ and $q>1$, as well as for the product of four particular nonterminating basic hypergeometric functions $ _2\phi _1$.

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English version:
Theoretical and Mathematical Physics, 1995, 105:3, 1500–1508

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Received: 01.03.1995

Citation: N. M. Atakishiyev, “Ramanujan-type continuous measures for classical $q$-polynomials”, TMF, 105:3 (1995), 383–392; Theoret. and Math. Phys., 105:3 (1995), 1500–1508

Citation in format AMSBIB
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\by N.~M.~Atakishiyev
\paper Ramanujan-type continuous measures for classical $q$-polynomials
\jour TMF
\yr 1995
\vol 105
\issue 3
\pages 383--392
\mathnet{http://mi.mathnet.ru/tmf1382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1605659}
\zmath{https://zbmath.org/?q=an:0898.33012}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 105
\issue 3
\pages 1500--1508
\crossref{https://doi.org/10.1007/BF02070870}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995VD44600004}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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