Simplifying coefficients in differential equations for generating function of Catalan numbers
In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2019.1663782 |
| _version_ | 1818310758916685824 |
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| author | Feng Qi Yong-Hong Yao |
| author_facet | Feng Qi Yong-Hong Yao |
| author_sort | Feng Qi |
| collection | DOAJ |
| description | In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers. |
| first_indexed | 2024-12-13T07:51:10Z |
| format | Article |
| id | doaj.art-4bba5042ee704d089b5f4461b6751d62 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-12-13T07:51:10Z |
| publishDate | 2019-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-4bba5042ee704d089b5f4461b6751d622022-12-21T23:54:40ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552019-12-0113194795010.1080/16583655.2019.16637821663782Simplifying coefficients in differential equations for generating function of Catalan numbersFeng Qi0Yong-Hong Yao1Henan Polytechnic UniversityTianjin Polytechnic UniversityIn the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.http://dx.doi.org/10.1080/16583655.2019.1663782simplifyingcoefficientnonlinear ordinary differential equationgenerating functioncatalan numberfaà di bruno formulabell polynomial of the second kindinversion theorem |
| spellingShingle | Feng Qi Yong-Hong Yao Simplifying coefficients in differential equations for generating function of Catalan numbers Journal of Taibah University for Science simplifying coefficient nonlinear ordinary differential equation generating function catalan number faà di bruno formula bell polynomial of the second kind inversion theorem |
| title | Simplifying coefficients in differential equations for generating function of Catalan numbers |
| title_full | Simplifying coefficients in differential equations for generating function of Catalan numbers |
| title_fullStr | Simplifying coefficients in differential equations for generating function of Catalan numbers |
| title_full_unstemmed | Simplifying coefficients in differential equations for generating function of Catalan numbers |
| title_short | Simplifying coefficients in differential equations for generating function of Catalan numbers |
| title_sort | simplifying coefficients in differential equations for generating function of catalan numbers |
| topic | simplifying coefficient nonlinear ordinary differential equation generating function catalan number faà di bruno formula bell polynomial of the second kind inversion theorem |
| url | http://dx.doi.org/10.1080/16583655.2019.1663782 |
| work_keys_str_mv | AT fengqi simplifyingcoefficientsindifferentialequationsforgeneratingfunctionofcatalannumbers AT yonghongyao simplifyingcoefficientsindifferentialequationsforgeneratingfunctionofcatalannumbers |