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)

Label
Generalized associated Legendre functions and their applications
Title
Generalized associated Legendre functions and their applications
Statement of responsibility
Nina Virchenko, Iryna Fedotova
Creator
Contributor
Subject
Genre
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 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 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)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 183-191) 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 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
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)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 183-191) 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 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
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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