Some combinatorial identities containing central binomial coefficients or Catalan numbers*
In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four sum formulas for finite sums contain...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2023-12-01
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| Series: | Applied Mathematics in Science and Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/27690911.2023.2204233 |
| _version_ | 1797641038872969216 |
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| author | Feng Qi Da-Wei Niu Dongkyu Lim |
| author_facet | Feng Qi Da-Wei Niu Dongkyu Lim |
| author_sort | Feng Qi |
| collection | DOAJ |
| description | In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four sum formulas for finite sums containing the ratio or product of two central binomial coefficients or the Catalan numbers. The instant proof simplifies discussions in the journal papers: College Math. J. 43 (2012), no. 2, 141–146; Amer. Math. Monthly 121 (2014), no. 3, 267–267; Amer. Math. Monthly 123 (2016), no. 4, 405–406; Elem. Math. 71 (2016), no. 3, 109–121; and Mathematics 5 (2017), no. 3, Article 40, 31 pages. |
| first_indexed | 2024-03-11T13:39:52Z |
| format | Article |
| id | doaj.art-e36ec65084f74f1a97b0e592a90e6ac7 |
| institution | Directory Open Access Journal |
| issn | 2769-0911 |
| language | English |
| last_indexed | 2024-03-11T13:39:52Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj.art-e36ec65084f74f1a97b0e592a90e6ac72023-11-02T13:48:31ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112023-12-0131110.1080/27690911.2023.22042332204233Some combinatorial identities containing central binomial coefficients or Catalan numbers*Feng Qi0Da-Wei Niu1Dongkyu Lim2Henan Polytechnic UniversityHenan University of Animal Husbandry and EconomyAndong National UniversityIn the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four sum formulas for finite sums containing the ratio or product of two central binomial coefficients or the Catalan numbers. The instant proof simplifies discussions in the journal papers: College Math. J. 43 (2012), no. 2, 141–146; Amer. Math. Monthly 121 (2014), no. 3, 267–267; Amer. Math. Monthly 123 (2016), no. 4, 405–406; Elem. Math. 71 (2016), no. 3, 109–121; and Mathematics 5 (2017), no. 3, Article 40, 31 pages.http://dx.doi.org/10.1080/27690911.2023.2204233catalan numberarcsinesquarecubicratioproductsum formulacentral binomial coefficientfinite summaclaurin's expansion |
| spellingShingle | Feng Qi Da-Wei Niu Dongkyu Lim Some combinatorial identities containing central binomial coefficients or Catalan numbers* Applied Mathematics in Science and Engineering catalan number arcsine square cubic ratio product sum formula central binomial coefficient finite sum maclaurin's expansion |
| title | Some combinatorial identities containing central binomial coefficients or Catalan numbers* |
| title_full | Some combinatorial identities containing central binomial coefficients or Catalan numbers* |
| title_fullStr | Some combinatorial identities containing central binomial coefficients or Catalan numbers* |
| title_full_unstemmed | Some combinatorial identities containing central binomial coefficients or Catalan numbers* |
| title_short | Some combinatorial identities containing central binomial coefficients or Catalan numbers* |
| title_sort | some combinatorial identities containing central binomial coefficients or catalan numbers |
| topic | catalan number arcsine square cubic ratio product sum formula central binomial coefficient finite sum maclaurin's expansion |
| url | http://dx.doi.org/10.1080/27690911.2023.2204233 |
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