Generalized associated Legendre functions and their applications:
"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 Bes...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2001
|
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | "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 ρFq, 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 associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(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 Legnedre functions as their series representations, asymptotic formulas in a neighborhood 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,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc." |
| Beschreibung: | xx, 195 p. ill., ports |
| ISBN: | 9789812811783 |
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| 100 | 1 | |a Virchenko, N. O. |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 Pub. Co. |c c2001 | |
| 300 | |a xx, 195 p. |b ill., ports | ||
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| 520 | |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 ρFq, 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 associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(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 Legnedre functions as their series representations, asymptotic formulas in a neighborhood 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,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc." | ||
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Datensatz im Suchindex
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| author | Virchenko, N. O. |
| author_facet | Virchenko, N. O. |
| author_role | aut |
| author_sort | Virchenko, N. O. |
| author_variant | n o v no nov |
| building | Verbundindex |
| bvnumber | BV044636225 |
| classification_rvk | SK 680 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00004364 (OCoLC)740729467 (DE-599)BVBBV044636225 |
| 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 | 3515.53 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044636225 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:57:48Z |
| institution | BVB |
| isbn | 9789812811783 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030034195 |
| oclc_num | 740729467 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xx, 195 p. ill., ports |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Virchenko, N. O. Verfasser aut Generalized associated Legendre functions and their applications Nina Virchenko, Iryna Fedotova Singapore World Scientific Pub. Co. c2001 xx, 195 p. ill., ports txt rdacontent c rdamedia cr rdacarrier "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 ρFq, 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 associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(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 Legnedre functions as their series representations, asymptotic formulas in a neighborhood 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,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc." Legendre's functions Fedotova, Iryna Sonstige oth Erscheint auch als Druck-Ausgabe 9789810243531 Erscheint auch als Druck-Ausgabe 9810243537 http://www.worldscientific.com/worldscibooks/10.1142/4463#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Virchenko, N. O. Generalized associated Legendre functions and their applications 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's functions |
| topic_facet | Legendre's functions |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4463#t=toc |
| work_keys_str_mv | AT virchenkono generalizedassociatedlegendrefunctionsandtheirapplications AT fedotovairyna generalizedassociatedlegendrefunctionsandtheirapplications |