04820nam 2200637Ia 450 991078238940332120230607222130.01-281-96072-19786611960728981-281-178-8(CKB)1000000000538094(EBL)1681575(SSID)ssj0000161421(PQKBManifestationID)11155006(PQKBTitleCode)TC0000161421(PQKBWorkID)10197882(PQKB)11271185(MiAaPQ)EBC1681575(WSP)00004463(Au-PeEL)EBL1681575(CaPaEBR)ebr10255792(CaONFJC)MIL196072(OCoLC)815756570(EXLCZ)99100000000053809420010718d2001 uy 0engur|n|---|||||txtccrGeneralized associated Legendre functions and their applications[electronic resource] /Nina Virchenko, Iryna FedotovaSingapore ;River Edge, N.J. World Scientificc20011 online resource (217 p.)Description based upon print version of record.981-02-4353-7 Includes bibliographical references (p. 183-191) and index.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 equation7. 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 functions13. 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 applications25. Examples of the integrals involving the generalized associated Legendre functionsAppendix. The hypergeometric function; Bibliography; Subject indexThe 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 closedLegendre's functionsSpherical harmonicsLegendre's functions.Spherical harmonics.515.53Virchenko N. O(Nina Opanasivna)486847Fedotova Iryna734232MiAaPQMiAaPQMiAaPQBOOK9910782389403321Generalized associated Legendre functions and their applications1449052UNINA