On Parameter Differentiation for Integral Representations of Associated Legendre Functions

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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dc.contributor.author	Cohl, H.S.
dc.date.accessioned	2019-02-13T18:18:07Z
dc.date.available	2019-02-13T18:18:07Z
dc.date.issued	2011
dc.identifier.citation	On Parameter Differentiation for Integral Representations of Associated Legendre Functions / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 31B05; 31B10; 33B10; 33B15; 33C05; 33C10
dc.identifier.other	DOI:10.3842/SIGMA.2011.050
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147177
dc.description.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\{−1,1}→C given by f(z)=z/(√(z+1)√(z−1)).	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. I would like to thank Dr. A.F.M. ter Elst for extremely valuable discussions and acknowledge funding for time to write this paper from the Dean of the Faculty of Science at the University of Auckland in the form of a three month stipend to enhance University of Auckland 2012 PBRF Performance. I would like to express my gratitude to the anonymous referees whose helpful comments improved this paper. I would also like to thank F.W.J. Olver for helpful discussions. Part of this work was conducted while the author was a National Research Council Research Postdoctoral Associate in the Information Technology Laboratory of the National Institute of Standards and Technology.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On Parameter Differentiation for Integral Representations of Associated Legendre Functions	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA