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)

DOI10.1007/S10910-011-9826-3zbMath1304.33006arXiv0907.3217OpenAlexW3103255472MaRDI QIDQ645140

Radosław Szmytkowski

Publication date: 8 November 2011

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.3217

zbMATH Keywords

spherical harmonicsLegendre functionsspecial functionsparameter derivatives

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (9)

A note on parameter derivatives of the Jacobi polynomials on the triangle ⋮ On parameter derivatives of a family of polynomials in two variables ⋮ On a class of monogenic functions with (logarithmic) line singularities ⋮ Representations for parameter derivatives of some Koornwinder polynomials in two variables ⋮ Special classes of monogenic functions in \(\mathbb {H}\) ⋮ Oblique derivative problems for elliptic equations on conical domains ⋮ 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) ⋮ Gegenbauer expansions and addition theorems for a binomial and logarithmic fundamental solution of the even-dimensional Euclidean polyharmonic equation ⋮ Fourier expansions for a logarithmic fundamental solution of the polyharmonic equation

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• The Evaluation of Incomplete Normalization Integrals and Derivatives with Respect to the Order of Associated Legendre Polynomials
• Backscattering from Wide-Angle and Narrow-Angle Cones
• On the derivative of the Legendre function of the first kind with respect to its degree

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