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

DOI10.1080/10652460903445043zbMath1195.31006arXiv0911.5266OpenAlexW2019863466MaRDI QIDQ3584672

Howard S. Cohl

Publication date: 30 August 2010

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.5266

zbMATH Keywords

modified Bessel functionsderivativesLegendre functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Exponential and trigonometric functions (33B10)

Related Items (4)

On the order derivatives of Bessel functions ⋮ 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) ⋮ 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

Cites Work

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• 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)
• Developments in determining the gravitational potential using toroidal functions
• On the derivatives of the Bessel and Struve functions with respect to the order
• Addendum to ‘On the derivative of the Legendre function of the first kind with respect to its degree’

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