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Generalized Associated Legendre Functions And Their Applications - Iryna Fedotova

Generalized Associated Legendre Functions And Their Applications

Hardcover Published: 3rd May 2001
ISBN: 9789810243531
Number Of Pages: 216

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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", 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.

Foreword
Preface
A general information on Legendre functionsp. 1
The generalized associated Legendre functionsp. 11
The series representations of the generalized associated Legendre functionsp. 17
Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutionsp. 25
Relations between contiguous generalized associated Legendre functionsp. 32
Differential operators generated by the generalized associated Legendre equationp. 35
Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular pointsp. 40
Asymptotic representations of the generalized associated Legendre functions as functions of parametersp. 48
Integral representations of the generalized associated Legendre functions of the first kindp. 54
Integral representations of the generalized associated Legendre functions of the second kindp. 60
Zeros of the generalized associated Legendre functionsp. 67
Connection of the generalized associated Legendre functions with the Jacobi functionsp. 71
Integral relations and series with the generalized associated Legendre functionsp. 78
Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functionsp. 88
Integral transforms with the generalized associated Legendre functionsp. 96
Dual integral equations with the generalized Legendre function of the first kind P[subscript -1/2+k[pi]][superscript m,n] (ch [alpha])p. 116
Dual integral equations with P[subscript -1/2+k[pi]][superscript m,n] (ch [alpha]) and the weight function [1 + G(tau)]p. 123
Triple integral equations with the generalized Legendre function of the first kind P[subscript -1/2+[pi]][superscript m,n] (ch [alpha])p. 126
Hybrid dual integral equationsp. 133
Systems of triple integral equations with the generalized associated Legendre functions of the first kind P[subscript -1/2+[pi]][superscript m,n] (ch [alpha])p. 137
On a property of the fractional Riemann-Liouville integral of P[subscript k][superscript m,n] (z)p. 144
On some generalized integral operators of Buschman-Erdelyi's typep. 147
Factorization of integral operators with the generalized associated Legendre functions and its application for solving integral equationsp. 152
Some generalizations of integral transforms of Mehler-Fock type and their applicationsp. 160
Examples of the integrals involving the generalized associated Legendre functionsp. 171
The hypergeometric functionp. 175
Bibliographyp. 183
Subject indexp. 193
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810243531
ISBN-10: 9810243537
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 216
Published: 3rd May 2001
Country of Publication: SG
Dimensions (cm): 22.61 x 16.2  x 1.7
Weight (kg): 0.42

Earn 405 Qantas Points
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