04854nam 2200649Ia 450 991045437800332120200520144314.01-281-96072-19786611960728981-281-178-8(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 harmonicsElectronic books.Legendre's functions.Spherical harmonics.515.53Virchenko N. O(Nina Opanasivna)944332Fedotova Iryna734232MiAaPQMiAaPQMiAaPQBOOK9910454378003321Generalized associated Legendre functions and their applications2131710UNINA01189nam 22003613 450 991013045340332120200313150550.088-596-0585-7(CKB)3400000000019749(ItFiC)it 02415170(EXLCZ)99340000000001974920101102d2009 uy 0itaGli ultimi testimoni storie e ricordi degli internati militari nei lager nazisti /a cura di Annarosa Bartolini, Emanuela Malvezzi ; con una introduzione di Paolo PezzinoFirenze Polistampa2009238 p. ill. ;24 cmQuaderni dell'Archivio storico / Città di Piombino ;4Interviews and war memoirs.Also cont. 2 diaries (p. 197-238).Includes bibliographical references.Gli ultimi testimoni940920365Bartolini Annarosa1025337Malvezzi Emanuela1025338Pezzino Paolo134319ItFiCItFiCBOOK9910130453403321Gli ultimi testimoni2437805UNINA