A note on parameter derivatives of classical orthogonal polynomials

2009/01/17 by Radoslaw Szmytkowski, Szmytkowski, Radoslaw
Mathematics · Physics and Astronomy · #33C45 #42C05 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:33C45 #msc:42C05 #msc:42C10

paper · pdf · doi:10.48550/arxiv.0901.2639

8 pages, LaTeX; one reference added, some references updated

arxiv created 2010/11/16 · arxiv updated 2010/11/17

Abstract

Coefficients in the expansions of the form ∂ P_n(λ;z)/∂λ=∑_k=0ⁿa_nk(λ)P_k(λ;z), where P_n(λ;z) is the nth classical (the generalized Laguerre, Gegenbauer or Jacobi) orthogonal polynomial of variable z and λ is a parameter, are evaluated. A method we adopt in the present paper differs from that used by Fröhlich [Integral Transforms Spec. Funct. 2 (1994) 253] for the Jacobi polynomials and by Koepf [Integral Transforms Spec. Funct. 5 (1997) 69] for the generalized Laguerre and the Gegenbauer polynomials.

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