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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 050, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.050
(Mi sigma608)
 

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
Full-text PDF (496 kB) Citations (4)
References:
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
Bibliographic databases:
Document Type: Article
Language: English
Citation: Howard S. Cohl, “On Parameter Differentiation for Integral Representations of Associated Legendre Functions”, SIGMA, 7 (2011), 050, 16 pp.
Citation in format AMSBIB
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\paper On Parameter Differentiation for Integral Representations of Associated Legendre Functions
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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