Derivatives with respect to the degree and order of associated Legendre functions for |z|>1 using modified Bessel functions

2009/11/27 by Howard S. Cohl, Cohl, Howard S.
Mathematics · #31B05 #31B10 #33B10 #33B15 #33C05 #33C10 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #math.CA #msc:31B05 #msc:31B10 #msc:33B10 #msc:33B15 #msc:33C05 #msc:33C10

paper · pdf · doi:10.48550/arxiv.0911.5266

7 pages. Accepted in Journal of Integral Transforms and Special Functions

arxiv created 2009/11/27 · openalex publication_date 2009/11/27 · arxiv updated 2009/12/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to compute derivatives of the associated Legendre functions with respect to their parameters. For the associated Legendre functions of the first and second kind, derivatives with respect to the degree are evaluated at odd-half-integer degrees, for general complex orders, and derivatives with respect to the order are evaluated at integer orders, for general complex degrees.

Related

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