Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V.

Si

J. Math. Anal. Appl.

Article

Científica

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1

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85062069909&doi=10.1016%2fj.jmaa.2019.01.068&partnerID=40&md5=d11bffa1658cb75975aeb0bd25004024

15/07/2019

000465168900001

2-s2.0-85062069909

10.1016/j.jmaa.2019.01.068

We derive a generalization of the Rogers generating function for the continuous q-ultraspherical/Rogers polynomials whose coefficient is a 2 phi 1. From that expansion, we derive corresponding specialization and limit transition expansions for the continuous q-Hermite, continuous q-Legendre, Laguerre, and Chebyshev polynomials of the first kind. Using a generalized expansion of the Rogers generating function in terms of the Askey Wilson polynomials by Ismail & Simeonov whose coefficient is a 807, we derive corresponding generalized expansions for the Wilson, continuous q-Jacobi, and Jacobi polynomials. By comparing the coefficients of the Askey Wilson expansion to our continuous q-ultraspherical/Rogers expansion, we derive a new quadratic transformation for basic hypergeometric functions which relates an 8 phi 7 to a 2 phi 1. We also obtain several definite integral representations which correspond to the above mentioned expansions through the use of orthogonality. Published by Elsevier Inc.

Basic hypergeometric series; Basic hypergeometric orthogonal polynomials; Generating functions; Connection coefficients; Eigenfunction expansions; Definite integrals

• ROBERTO SANTIAGO COSTAS SANTOS