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 Bessel, M...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, N.J. :
World Scientific,
©2001.
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| Online-Zugang: | 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 "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 resource (xx, 195 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 183-191) and index. |
| ISBN: | 9789812811783 9812811788 1281960721 9781281960726 |
Internformat
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| 245 | 1 | 0 | |a Generalized associated Legendre functions and their applications / |c Nina Virchenko, Iryna Fedotova. |
| 260 | |a Singapore ; |a River Edge, N.J. : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xx, 195 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 183-191) and index. | ||
| 588 | 0 | |a Print version record. | |
| 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 "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 | ||
| 505 | 0 | |a 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 points -- 8. 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 functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions. | |
| 650 | 0 | |a Legendre's functions. |0 http://id.loc.gov/authorities/subjects/sh85075778 | |
| 650 | 6 | |a Fonctions de Legendre. | |
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| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Legendre's functions |2 fast | |
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Datensatz im Suchindex
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| _version_ | 1816881678733279232 |
| adam_text | |
| any_adam_object | |
| author | Virchenko, N. O. (Nina Opanasivna) |
| author2 | Fedotova, Iryna |
| author2_role | |
| author2_variant | i f if |
| author_GND | http://id.loc.gov/authorities/names/n78049234 http://id.loc.gov/authorities/names/no2001081271 |
| author_facet | Virchenko, N. O. (Nina Opanasivna) Fedotova, Iryna |
| author_role | |
| author_sort | Virchenko, N. O. |
| author_variant | n o v no nov |
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| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| 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 points -- 8. 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 functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions. |
| ctrlnum | (OCoLC)261340331 |
| 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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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. 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| id | ZDB-4-EBA-ocn261340331 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:32Z |
| institution | BVB |
| isbn | 9789812811783 9812811788 1281960721 9781281960726 |
| language | English |
| oclc_num | 261340331 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xx, 195 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Virchenko, N. O. (Nina Opanasivna) https://id.oclc.org/worldcat/entity/E39PCjrBcFQYxw9YFgcqh983cP http://id.loc.gov/authorities/names/n78049234 Generalized associated Legendre functions and their applications / Nina Virchenko, Iryna Fedotova. Singapore ; River Edge, N.J. : World Scientific, ©2001. 1 online resource (xx, 195 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 183-191) and index. Print version record. 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 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 points -- 8. 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 functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions. Legendre's functions. http://id.loc.gov/authorities/subjects/sh85075778 Fonctions de Legendre. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Legendre's functions fast Fedotova, Iryna. https://id.oclc.org/worldcat/entity/E39PCjJgK6c7Dy9xJVCcYvhBrq http://id.loc.gov/authorities/names/no2001081271 has work: Generalized associated Legendre functions and their applications (Text) https://id.oclc.org/worldcat/entity/E39PCFrpqJrJrXfqKTBkXTqWjC https://id.oclc.org/worldcat/ontology/hasWork Print version: Virchenko, N.O. (Nina Opanasivna). Generalized associated Legendre functions and their applications. Singapore ; River Edge, N.J. : World Scientific, ©2001 9810243537 9789810243531 (DLC) 2001275225 (OCoLC)47401005 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235905 Volltext |
| spellingShingle | Virchenko, N. O. (Nina Opanasivna) Generalized associated Legendre functions and their applications / 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 points -- 8. 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 functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions. Legendre's functions. http://id.loc.gov/authorities/subjects/sh85075778 Fonctions de Legendre. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Legendre's functions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85075778 |
| 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. http://id.loc.gov/authorities/subjects/sh85075778 Fonctions de Legendre. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Legendre's functions fast |
| topic_facet | Legendre's functions. Fonctions de Legendre. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Legendre's functions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235905 |
| work_keys_str_mv | AT virchenkono generalizedassociatedlegendrefunctionsandtheirapplications AT fedotovairyna generalizedassociatedlegendrefunctionsandtheirapplications |