Parametric Integrals for Binomial Series with Harmonic Polynomials
Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients and harmonic numbers. Most of the values for...
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MDPI AG
2024-12-01
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| author | Chunli Li Wenchang Chu |
| author_facet | Chunli Li Wenchang Chu |
| author_sort | Chunli Li |
| collection | DOAJ |
| description | Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients and harmonic numbers. Most of the values for binomial series found in this paper concern the dilogarithm and trilogarithm functions. |
| format | Article |
| id | doaj-art-9a09f31ec4984b1f9b7495c8b8cd4b33 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-9a09f31ec4984b1f9b7495c8b8cd4b332024-12-27T14:10:30ZengMDPI AGAxioms2075-16802024-12-01131288510.3390/axioms13120885Parametric Integrals for Binomial Series with Harmonic PolynomialsChunli Li0Wenchang Chu1School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, ChinaIndependent Researcher, 73100 Lecce, ItalyBinomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients and harmonic numbers. Most of the values for binomial series found in this paper concern the dilogarithm and trilogarithm functions.https://www.mdpi.com/2075-1680/13/12/885binomial seriesharmonic numberbisection seriesparametric integralpolylogarithm |
| spellingShingle | Chunli Li Wenchang Chu Parametric Integrals for Binomial Series with Harmonic Polynomials Axioms binomial series harmonic number bisection series parametric integral polylogarithm |
| title | Parametric Integrals for Binomial Series with Harmonic Polynomials |
| title_full | Parametric Integrals for Binomial Series with Harmonic Polynomials |
| title_fullStr | Parametric Integrals for Binomial Series with Harmonic Polynomials |
| title_full_unstemmed | Parametric Integrals for Binomial Series with Harmonic Polynomials |
| title_short | Parametric Integrals for Binomial Series with Harmonic Polynomials |
| title_sort | parametric integrals for binomial series with harmonic polynomials |
| topic | binomial series harmonic number bisection series parametric integral polylogarithm |
| url | https://www.mdpi.com/2075-1680/13/12/885 |
| work_keys_str_mv | AT chunlili parametricintegralsforbinomialserieswithharmonicpolynomials AT wenchangchu parametricintegralsforbinomialserieswithharmonicpolynomials |