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Generalized associated Legendre functions and their applications [[electronic resource] /] / Nina Virchenko, Iryna Fedotova
| Generalized associated Legendre functions and their applications [[electronic resource] /] / Nina Virchenko, Iryna Fedotova |
| Autore | Virchenko N. O (Nina Opanasivna) |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (217 p.) |
| Disciplina | 515.53 |
| Altri autori (Persone) | FedotovaIryna |
| Soggetto topico |
Legendre's functions
Spherical harmonics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-96072-1
9786611960728 981-281-178-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910454378003321 |
Virchenko N. O (Nina Opanasivna)
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized associated Legendre functions and their applications [[electronic resource] /] / Nina Virchenko, Iryna Fedotova
| Generalized associated Legendre functions and their applications [[electronic resource] /] / Nina Virchenko, Iryna Fedotova |
| Autore | Virchenko N. O (Nina Opanasivna) |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (217 p.) |
| Disciplina | 515.53 |
| Altri autori (Persone) | FedotovaIryna |
| Soggetto topico |
Legendre's functions
Spherical harmonics |
| ISBN |
1-281-96072-1
9786611960728 981-281-178-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910782389403321 |
|
Virchenko N. O (Nina Opanasivna)
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||