Foto: Generalized associated legendre functions and their applications

Generalized associated legendre functions and their applications.

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Books boeken iryna fedotova world scientific publishing hardcover 2001: 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 Fq Meijers G-function Foxs 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 Pmn z and Qmn 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 Pmn z and Qmn z the classes of dual and triple integral equations associated with the function Pmn-12i ch etc.

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Generalized associated legendre functions and their applications.

Applications

Generalized

Associated

Functions

Legendre

Generalized functions theory and applications.

Chapman hallcrc research notes in mathematics series nonlinear theory of generalized functions.

Asymptotic behavior of generalized functions.

Computation of generalized matrix inverses and applications.

Generalized functions and fourier analysis.