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Generalized associated Legendre functions and their applications

Author: N O Virchenko; Iryna Fedotova
Publisher: Singapore ; River Edge, N.J. : World Scientific, ©2001.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions "YFq",  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Virchenko, N.O. (Nina Opanasivna).
Generalized associated Legendre functions and their applications.
Singapore ; River Edge, N.J. : World Scientific, ©2001
(DLC) 2001275225
(OCoLC)47401005
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: N O Virchenko; Iryna Fedotova
ISBN: 9789812811783 9812811788 1281960721 9781281960726
OCLC Number: 261340331
Description: 1 online resource (xx, 195 pages) : illustrations
Contents: 1. A general information on Legendre functions --
2. The generalized associated Legendre functions --
3. The series representations of the generalized associated Legendre functions --
4. Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutions --
5. Relations between contiguous generalized associated Legendre functions --
6. Differential operators generated by the generalized associated Legendre equation --
7. Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular points --
8. Asymptotic representations of the generalized associated Legendre functions as functions of parameters --
9. Integral representations of the generalized associated Legendre functions of the first kind --
10. Integral representations of the generalized associated Legendre functions of the second kind --
11. Zeros of the generalized associated Legendre functions --
12. Connection of the generalized associated Legendre functions with the Jacobi functions --
13. Integral relations and series with the generalized associated Legendre functions --
14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions --
15. Integral transforms with the generalized associated Legendre functions.
Responsibility: Nina Virchenko, Iryna Fedotova.

Abstract:

This text deals with the theory and applications of generalized associated Legendre functions of the first and the second kind. It also presents the theory of factorization and composition structure  Read more...

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