GENERALIZED ASSOCIATED LEGENDRE FUNCTIONS AND THEIR APPLICATIONS - Hardcover

Fedotova, Iryna; Virchenko, Nina

Hardcover

ISBN 10: 9810243537 ISBN 13: 9789810243531

Publisher: World Scientific Publishing Company, 2001

Synopsis

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 ρFq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm, nκ(z) and Qm, nκ(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm, nκ(z) and Qm, nκ(z), the classes of dual and triple integral equations associated with the function Pm, n-1/2+iς(chα) etc.

About this title

Review

"The authors have done a good job of presenting technical material in a systematic and readable form." -- SIAM Review, 2002

The book is printed nicely and will be very useful to researchers concerned with special functions and allied topics. -- Mathematical Reviews, 2002

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2001
• Language: English
• ISBN 10: 9810243537
• ISBN 13: 9789810243531
• Binding: Hardcover
• Edition number: 1
• Number of pages: 216