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This article is cited in 4 scientific papers (total in 4 papers)
On Parameter Differentiation for Integral Representations of Associated Legendre Functions
Howard S. Cohlab a Applied and Computational Mathematics Division, Information Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, USA
b Department of Mathematics, University of Auckland, 38 Princes Str., Auckland, New Zealand
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 $f:\mathbb C\setminus\{-1,1\}\to\mathbb C$ given by $f(z)=z/(\sqrt{z+1}\sqrt{z-1})$.
Keywords:
Legendre functions; modified Bessel functions; derivatives.
Received: January 19, 2011; in final form May 4, 2011; Published online May 24, 2011
Citation:
Howard S. Cohl, “On Parameter Differentiation for Integral Representations of Associated Legendre Functions”, SIGMA, 7 (2011), 050, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma608 https://www.mathnet.ru/eng/sigma/v7/p50
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Abstract page: | 228 | Full-text PDF : | 64 | References: | 44 |
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