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The Resource Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource)
Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource)
Resource Information
The item Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 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 wellknown 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
 Language

 eng
 eng
 Extent
 1 online resource (217 p.)
 Note
 Description based upon print version of record
 Contents

 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 Bfunctions; 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 RiemannLiouville integral of Pm,n k (z); 22. On some generalized integral operators of BuschmanErdélyi'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 MehlerFock type and their applications
 25. Examples of the integrals involving the generalized associated Legendre functionsAppendix. The hypergeometric function; Bibliography; Subject index
 Isbn
 9781281960726
 Label
 Generalized associated Legendre functions and their applications
 Title
 Generalized associated Legendre functions and their applications
 Statement of responsibility
 Nina Virchenko, Iryna Fedotova
 Language

 eng
 eng
 Summary
 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 wellknown 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
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Virchenko, N. O.
 Dewey number
 515.53
 Illustrations

 illustrations
 portraits
 Index
 index present
 Language note
 English
 LC call number
 QA406
 LC item number
 .V57 2001
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Fedotova, Iryna
 http://library.link/vocab/subjectName

 Legendre's functions
 Spherical harmonics
 Label
 Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 183191) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 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 Bfunctions; 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 RiemannLiouville integral of Pm,n k (z); 22. On some generalized integral operators of BuschmanErdélyi'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 MehlerFock type and their applications
 25. Examples of the integrals involving the generalized associated Legendre functionsAppendix. The hypergeometric function; Bibliography; Subject index
 Dimensions
 unknown
 Extent
 1 online resource (217 p.)
 Form of item
 online
 Isbn
 9781281960726
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)1000000000538094
 (EBL)1681575
 (SSID)ssj0000161421
 (PQKBManifestationID)11155006
 (PQKBTitleCode)TC0000161421
 (PQKBWorkID)10197882
 (PQKB)11271185
 (MiAaPQ)EBC1681575
 (WSP)00004463
 (EXLCZ)991000000000538094
 Label
 Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 183191) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 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 Bfunctions; 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 RiemannLiouville integral of Pm,n k (z); 22. On some generalized integral operators of BuschmanErdélyi'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 MehlerFock type and their applications
 25. Examples of the integrals involving the generalized associated Legendre functionsAppendix. The hypergeometric function; Bibliography; Subject index
 Dimensions
 unknown
 Extent
 1 online resource (217 p.)
 Form of item
 online
 Isbn
 9781281960726
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)1000000000538094
 (EBL)1681575
 (SSID)ssj0000161421
 (PQKBManifestationID)11155006
 (PQKBTitleCode)TC0000161421
 (PQKBWorkID)10197882
 (PQKB)11271185
 (MiAaPQ)EBC1681575
 (WSP)00004463
 (EXLCZ)991000000000538094
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/GeneralizedassociatedLegendrefunctionsand/I00fGxrX0LE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/GeneralizedassociatedLegendrefunctionsand/I00fGxrX0LE/">Generalized associated Legendre functions and their applications, Nina Virchenko, Iryna Fedotova, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>