| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910454378003321 |
|
|
Autore |
Virchenko N. O (Nina Opanasivna) |
|
|
Titolo |
Generalized associated Legendre functions and their applications [[electronic resource] /] / Nina Virchenko, Iryna Fedotova |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
|
|
|
|
|
|
|
ISBN |
|
1-281-96072-1 |
9786611960728 |
981-281-178-8 |
|
|
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (217 p.) |
|
|
|
|
|
|
Altri autori (Persone) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Legendre's functions |
Spherical harmonics |
Electronic books. |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (p. 183-191) and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Foreword; Preface; Contents; 1. A general information on Legendre functions; 2. The generalized associated Legendre functions; 3. The series representations of the generalized associated Legendre functions; 4. Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutions; 5. Relations between contiguous generalized associated Legendre functions; 6. Differential operators generated by the generalized associated Legendre equation |
7. Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular points8. Asymptotic representations of the generalized associated Legendre functions as functions of parameters; 9. Integral representations of the generalized associated Legendre functions of the first kind; 10. Integral representations of the generalized associated Legendre functions of the second kind; 11. Zeros of the generalized associated Legendre functions; 12. Connection of the generalized associated Legendre functions with the Jacobi functions |
13. Integral relations and series with the generalized associated Legendre functions14. Relations between the generalized associated |
|
|
|
|
|
|
|
|
|
|
|
Legendre functions Bessel functions elliptic integrals and incomplete B-functions; 15. Integral transforms with the generalized associated Legendre functions; 16. Dual integral equations with the generalized Legendre function of the first kind Pm,n -1/2+iτ(chα); 17. Dual integral equations with Pm,n -1/2+iτ(chα) and the weight function [1 + G(τ)]; 18. Triple integral equations with the generalized Legendre function of the first kind Pm,n -1/2+iτ(chα) |
19. Hybrid dual integral equations20. Systems of triple integral equations with the generalized associated Legendre functions of the first kind Pm,n -1/2+iτ(chα); 21. On a property of the fractional Riemann-Liouville integral of Pm,n k (z); 22. On some generalized integral operators of Buschman-Erdélyi's type; 23. Factorization of integral operators with the generalized associated Legendre functions and its application for solving integral equations; 24. Some generalizations of integral transforms of Mehler-Fock type and their applications |
25. Examples of the integrals involving the generalized associated Legendre functionsAppendix. The hypergeometric function; Bibliography; Subject index |
|
|
|
|
|
|
Sommario/riassunto |
|
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 , 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 |
|
|
|
|
|
|
|
| |