New mixed recurrence relations of two-variable orthogonal polynomials via differential operators

2020/09/23 by Mosaed M. Makky, Makky, Mosaed M., Mohammad Afzal Shadab +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CA #msc:11B37 #msc:33C45 #msc:33C47

paper · pdf · doi:10.48550/arxiv.2009.11269

10 pages, 0 figure

arxiv created 2020/09/23 · arxiv updated 2020/09/24

Abstract

In this paper, we derive new recurrence relations for two-variable orthogonal polynomials for example Jacobi polynomial, Bateman's polynomial and Legendre polynomial via two different differential operators Ξ=((∂ )/(∂ z) +√(w) (∂ )/(∂ w) ) and Δ=((1)/(w) (∂ )/(∂ z) +(1)/(z) (∂ )/(∂ w) ). We also derive some special cases of our main results.

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