Generalized Associated Legendre Functions and Their Applications - ISBN:9810243537

Generalized Associated Legendre Functions and Their Applications

Date: 30 April 2011, 07:58

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Review "The authors have done a good job of presenting technical material in a systematic and readable form." -- SIAM Review, 2002The book is printed nicely and will be very useful to researchers concerned with special functions and allied topics. -- Mathematical Reviews, 2002Product DescriptionThe 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", 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 Legendre functions of the first and the second kind, "Pm,nN(Z)" and "Qm,nN(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 Legendre functions as their series representations, asymptotic formulas in a neighbourhood 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,nN(Z)" and "Qm,nN(Z)", the classes of dual and triple integral equations associated with the function "Pm,n-1/2+/omega(chdelta)" etc.

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