Generalized Log-sine integrals and Bell polynomials
| Autor: | Orr, Derek |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | J. Comp. Appl. Math. 347 (2019) 330-342 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.cam.2018.08.026 |
| Popis: | In this paper, we investigate the integral of $x^n\log^m(\sin(x))$ for natural numbers $m$ and $n$. In doing so, we recover some well-known results and remark on some relations to the log-sine integral $\operatorname{Ls}_{n+m+1}^{(n)}(\theta)$. Later, we use properties of Bell polynomials to find a closed expression for the derivative of the central binomial and shifted central binomial coefficients in terms of polygamma functions and harmonic numbers. Comment: 19 pages |
| Databáze: | arXiv |
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