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

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

2009-11-27

arxiv.org/abs/0911.5266v1

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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.

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