Generalizations of generating functions for hypergeometric orthogonal\n polynomials with definite integrals

2013/02/11 by Howard S. Cohl, Cohl, Howard S., Connor MacKenzie +3
Mathematics · #05A15 #30E20 #33C20 #33C45 #34L10 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1302.2474

openalex publication_date 2013/02/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We generalize generating functions for hypergeometric orthogonal polynomials,\nnamely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These\ngeneralizations of generating functions are accomplished through series\nrearrangement using connection relations with one free parameter for these\northogonal polynomials. We also use orthogonality relations to determine\ncorresponding definite integrals.\n

Related

• Generalizations of generating functions for basic hypergeometric orthogonal polynomials
• Generalizations and specializations of generating functions for Jacobi,\n Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
• Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
• Systems of orthogonal polynomials defined by hypergeometric type equations
• Some definite integrals involving Jacobi polynomials