Higher Derivatives of Airy Functions and of their Products
The problem of evaluating higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials that have arisen in explicit formulae for these derivatives are given in terms of particular values of Gegenbauer polynomials. A similar problem for products of Ai...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209530 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Higher Derivatives of Airy Functions and of their Products / E.G. Abramochkin, E.V. Razueva // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862693961884237824 |
|---|---|
| author | Abramochkin, E.G. Razueva, E.V. |
| author_facet | Abramochkin, E.G. Razueva, E.V. |
| citation_txt | Higher Derivatives of Airy Functions and of their Products / E.G. Abramochkin, E.V. Razueva // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The problem of evaluating higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials that have arisen in explicit formulae for these derivatives are given in terms of particular values of Gegenbauer polynomials. A similar problem for products of Airy functions is solved in terms of terminating hypergeometric series.
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| first_indexed | 2025-12-07T16:21:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209530 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:21:24Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Abramochkin, E.G. Razueva, E.V. 2025-11-24T10:42:57Z 2018 Higher Derivatives of Airy Functions and of their Products / E.G. Abramochkin, E.V. Razueva // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 26 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C10; 33C05; 33C20 arXiv: 1707.05218 https://nasplib.isofts.kiev.ua/handle/123456789/209530 https://doi.org/10.3842/SIGMA.2018.042 The problem of evaluating higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials that have arisen in explicit formulae for these derivatives are given in terms of particular values of Gegenbauer polynomials. A similar problem for products of Airy functions is solved in terms of terminating hypergeometric series. The authors are grateful to Professor S.K. Suslov for his valuable comments that helped to improve the manuscript. The authors also thank the anonymous referees for their constructive criticisms and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Higher Derivatives of Airy Functions and of their Products Article published earlier |
| spellingShingle | Higher Derivatives of Airy Functions and of their Products Abramochkin, E.G. Razueva, E.V. |
| title | Higher Derivatives of Airy Functions and of their Products |
| title_full | Higher Derivatives of Airy Functions and of their Products |
| title_fullStr | Higher Derivatives of Airy Functions and of their Products |
| title_full_unstemmed | Higher Derivatives of Airy Functions and of their Products |
| title_short | Higher Derivatives of Airy Functions and of their Products |
| title_sort | higher derivatives of airy functions and of their products |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209530 |
| work_keys_str_mv | AT abramochkineg higherderivativesofairyfunctionsandoftheirproducts AT razuevaev higherderivativesofairyfunctionsandoftheirproducts |