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Publication Citation: On Parameter Differentiation for Integral Representations of Associated Legendre Functions

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Author(s): Howard S. Cohl;
Title: On Parameter Differentiation for Integral Representations of Associated Legendre Functions
Published: May 24, 2011
Abstract: For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind 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. We also discuss the properties of the complex function $f:\C\setminus\{-1,1\}\to\C$ given by $f(z)=z/(\sqrt{z+1}\sqrt{z-1})$.
Citation: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume: 7
Pages: 16 pp.
Keywords: Legendre functions; modified Bessel functions; derivatives
Research Areas: Math, Modeling
PDF version: PDF Document Click here to retrieve PDF version of paper (170KB)