On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

DOI10.1016/j.jmaa.2011.08.003zbMath1232.33005arXiv0910.4550OpenAlexW1975504715MaRDI QIDQ640977

Radosław Szmytkowski

Publication date: 21 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.4550

zbMATH Keywords

Jacobi polynomialsLegendre functionsparameter derivatives

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (5)

A note on parameter derivatives of the Jacobi polynomials on the triangle ⋮ On parameter derivatives of a family of polynomials in two variables ⋮ Representations for parameter derivatives of some Koornwinder polynomials in two variables ⋮ On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order) ⋮ On derivatives of hypergeometric functions and classical polynomials with respect to parameters

Uses Software

• DLMF

Cites Work

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• On parameter differentiation for integral representations of associated Legendre functions
• On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
• On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
• Green's function for the wavized Maxwell fish-eye problem
• On the derivatives of the Legendre functions and with respect to μ and ν
• Derivatives with respect to the degree and order of associated Legendre functions for |z|>1 using modified Bessel functions
• Addendum to ‘On the derivative of the Legendre function of the first kind with respect to its degree’
• On the derivative of the Legendre function of the first kind with respect to its degree

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