Generalized associated Legendre functions and their applications:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2001
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 183-191) and index 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 "YFq", 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 form, to examine these solutions, and to investigate the relationships between different classes of the special functions. This book deals with the theory and applications of generalized Legendre functions of the first and the second kind, "Pm, nN(Z)" and "Qm, nN(Z)", which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legendre functions as their series representations, asymptotic formulas in a neighbourhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions. The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions "Pm, nN(Z)" and "Qm, nN(Z)", the classes of dual and triple integral equations associated with the function "Pm, n-1/2+/omega(chdelta)" etc |
| Beschreibung: | 1 Online-Ressource (xx, 195 pages) |
| ISBN: | 1281960721 9781281960726 9789810243531 9789812811783 9810243537 9812811788 |
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| 100 | 1 | |a Virchenko, N. O., (Nina Opanasivna) |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized associated Legendre functions and their applications |c Nina Virchenko, Iryna Fedotova |
| 264 | 1 | |a Singapore |b World Scientific |c ©2001 | |
| 300 | |a 1 Online-Ressource (xx, 195 pages) | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (pages 183-191) and index | ||
| 500 | |a 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 "YFq", 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 form, to examine these solutions, and to investigate the relationships between different classes of the special functions. This book deals with the theory and applications of generalized Legendre functions of the first and the second kind, "Pm, nN(Z)" and "Qm, nN(Z)", which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legendre functions as their series representations, asymptotic formulas in a neighbourhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions. The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions "Pm, nN(Z)" and "Qm, nN(Z)", the classes of dual and triple integral equations associated with the function "Pm, n-1/2+/omega(chdelta)" etc | ||
| 650 | 4 | |a Legendre fonksiyonları | |
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 7 | |a Legendre's functions |2 fast | |
| 650 | 4 | |a Legendre's functions | |
| 700 | 1 | |a Fedotova, Iryna |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Virchenko, N. O., (Nina Opanasivna) |
| author_facet | Virchenko, N. O., (Nina Opanasivna) |
| author_role | aut |
| author_sort | Virchenko, N. O., (Nina Opanasivna) |
| author_variant | n o n o v nono nonov |
| building | Verbundindex |
| bvnumber | BV043087435 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)261340331 (DE-599)BVBBV043087435 |
| dewey-full | 515/.53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.53 |
| dewey-search | 515/.53 |
| dewey-sort | 3515 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043087435 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:02Z |
| institution | BVB |
| isbn | 1281960721 9781281960726 9789810243531 9789812811783 9810243537 9812811788 |
| language | English |
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| physical | 1 Online-Ressource (xx, 195 pages) |
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| spelling | Virchenko, N. O., (Nina Opanasivna) Verfasser aut Generalized associated Legendre functions and their applications Nina Virchenko, Iryna Fedotova Singapore World Scientific ©2001 1 Online-Ressource (xx, 195 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 183-191) and index 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 "YFq", 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 form, to examine these solutions, and to investigate the relationships between different classes of the special functions. This book deals with the theory and applications of generalized Legendre functions of the first and the second kind, "Pm, nN(Z)" and "Qm, nN(Z)", which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legendre functions as their series representations, asymptotic formulas in a neighbourhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions. The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions "Pm, nN(Z)" and "Qm, nN(Z)", the classes of dual and triple integral equations associated with the function "Pm, n-1/2+/omega(chdelta)" etc Legendre fonksiyonları MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Legendre's functions fast Legendre's functions Fedotova, Iryna Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235905 Aggregator Volltext |
| spellingShingle | Virchenko, N. O., (Nina Opanasivna) Generalized associated Legendre functions and their applications Legendre fonksiyonları MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Legendre's functions fast Legendre's functions |
| title | Generalized associated Legendre functions and their applications |
| title_auth | Generalized associated Legendre functions and their applications |
| title_exact_search | Generalized associated Legendre functions and their applications |
| title_full | Generalized associated Legendre functions and their applications Nina Virchenko, Iryna Fedotova |
| title_fullStr | Generalized associated Legendre functions and their applications Nina Virchenko, Iryna Fedotova |
| title_full_unstemmed | Generalized associated Legendre functions and their applications Nina Virchenko, Iryna Fedotova |
| title_short | Generalized associated Legendre functions and their applications |
| title_sort | generalized associated legendre functions and their applications |
| topic | Legendre fonksiyonları MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Legendre's functions fast Legendre's functions |
| topic_facet | Legendre fonksiyonları MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Legendre's functions |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235905 |
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