Generalizations of generating functions for basic hypergeometric orthogonal polynomials
Cohl, H. S., Costas-Santos, R. S., Hwang, P. R. and Wakhare, T. V. Open Journal of Mathematical Sciences 6 no. 1 (2022), 248– 261
Abstract
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.
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BibTeX
@article {cohlcostashwangwakhare2022,
AUTHOR={Cohl, H. S.; Costas-Santos, R. S.; Hwang, P. R. and Wakhare, T. V.},
TITLE={Generalizations of generating functions for basic hypergeometric orthogonal polynomials},
FJOURNAL={Open Journal of Mathematical Sciences},
VOLUME={6},
YEAR={2022},
NUMBER={1},
PAGES={248--261},
ISSN={2523-0212},
MSC={33D45; 05A15; 33D15; 33C45; 33C20; 34L10; 30E20}
DOI={10.30538/oms2022.0190},
URL={http://doi.org/10.30538/oms2022.0190},
}