Generalized Associated Legendre Functions and Their Applications
Nina Virchenko, Iryna Fedotova
194 pages, parution le 06/12/2001
Résumé
This book deals with the theory and applications of
generalized associated Legendre functions of the first and
the second kind, P[subscript K][superscript m,n](z) and
Q[subscript K][superscript m,n](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
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
P[subscript K][superscript m,n](z) and Q[subscript
K][superscript m,n](z), the classes of dual and triple
integral equations associated with the function P[subscript
-1/2+[pi]][superscript m,n] (ch[alpha]) etc...
Contents
- Foreword
- Preface
- 1 A general information on Legendre functions 1
- 2 The generalized associated Legendre functions 11
- 3 The series representations of the generalized associated Legendre functions 17
- 4 Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutions 25
- 5 Relations between contiguous generalized associated Legendre functions 32
- 6 Differential operators generated by the generalized associated Legendre equation 35
- 7 Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular points 40
- 8 Asymptotic representations of the generalized associated Legendre functions as functions of parameters 48
- 9 Integral representations of the generalized associated Legendre functions of the first kind 54
- 10 Integral representations of the generalized associated Legendre functions of the second kind 60
- 11 Zeros of the generalized associated Legendre functions 67
- 12 Connection of the generalized associated Legendre functions with the Jacobi functions 71
- 13 Integral relations and series with the generalized associated Legendre functions 78
- 14 Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions 88
- 15 Integral transforms with the generalized associated Legendre functions 96
- 16 Dual integral equations with the generalized Legendre function of the first kind P[subscript -1/2+k[pi]][superscript m,n] (ch [alpha]) 116
- 17 Dual integral equations with P[subscript -1/2+k[pi]][superscript m,n] (ch [alpha]) and the weight function [1 + G(tau)] 123
- 18 Triple integral equations with the generalized Legendre function of the first kind P[subscript -1/2+[pi]][superscript m,n] (ch [alpha]) 126
- 19 Hybrid dual integral equations 133
- 20 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]) 137
- 21 On a property of the fractional Riemann-Liouville integral of P[subscript k][superscript m,n] (z) 144
- 22 On some generalized integral operators of Buschman-Erdelyi's type 147
- 23 Factorization of integral operators with the generalized associated Legendre functions and its application for solving integral equations 152
- 24 Some generalizations of integral transforms of Mehler-Fock type and their applications 160
- 25 Examples of the integrals involving the generalized associated Legendre functions 171
- App The hypergeometric function 175
- Bibliography 183
- Subject index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | World Scientific |
| Auteur(s) | Nina Virchenko, Iryna Fedotova |
| Parution | 06/12/2001 |
| Nb. de pages | 194 |
| Format | 15,7 x 22,2 |
| Couverture | Relié |
| Poids | 400g |
| Intérieur | Noir et Blanc |
| EAN13 | 9789810243531 |
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