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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Virchenko, N.O. (Nina Opanasivna). Generalized associated Legendre functions and their applications. Singapore ; River Edge, N.J. : World Scientific, ©2001 (DLC) 2001275225 (OCoLC)47401005 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
N O Virchenko; Iryna Fedotova |

ISBN: | 9789812811783 9812811788 1281960721 9781281960726 |

OCLC Number: | 261340331 |

Description: | 1 online resource (xx, 195 pages) : illustrations |

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 points -- 8. 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 functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions. |

Responsibility: | Nina Virchenko, Iryna Fedotova. |

### Abstract:

This text deals with the theory and applications of generalized associated Legendre functions of the first and the second kind. It also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function.
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