Generalized Associated Legendre Function

Generalized Associated Legendre Function
1 463,- 1 463,-
Førpris 1829,- Spar 366,-
Førpris 1829,- Spar 366,-
Format E-Bok
Filformat PDF
Utgivelsesår 2001
Forlag World Scientific Publishing Co
Språk Engelsk
ISBN 9789812811783
Sider 216
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Om Generalized Associated Legendre Function

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. Contents:A General Information on Legendre FunctionsThe Generalized Associated Legendre FunctionsThe Series Representations of the Generalized Associated Legendre FunctionsRelations Between Different Solutions of the Generalized Legendre Equation. Wronskians of Linearly Independent SolutionsRelations Between Contiguous Generalized Associated Legendre FunctionsDifferential Operators Generated by the Generalized Associated Legendre EquationAsymptotic Formulas for the Generalized Associated Legendre Functions in a Neighborhood of Singular PointsAsymptotic Representations of the Generalized Associated Legendre Functions as the Functions of ParametersIntegral Representations of the Generalized Associated Legendre Functions of the First KindIntegral Representations of the Generalized Associated Legendre Functions of the Second KindZeros of the Generalized Associated Legendre FunctionsConnection of the Generalized Associated Legendre Functions with the Jacobi Functionsand other topicsReadership: Graduate students and researchers in mathematics, physics and engineering.Key Features:The book addresses the following three questions: what is the current state-of-the-art in this field; what are the advantages, capabilities and limitations of competing methods; what are the practical tools needed for spatially-resolved diffraction methods


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