Zobrazeno 1 - 10
of 282
pro vyhledávání: '"Glaisher–Kinkelin constant"'
Autor:
Pain, Jean-Christophe
We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. The calculations are based on definite integral expressions of $\log\Gamma(x)$, $\Gamma$ being the usual Gamma function, due respectively to F\'eaux and Kumme
Externí odkaz:
http://arxiv.org/abs/2410.22338
Autor:
Pain, Jean-Christophe
We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. Both are based on a definite integral of $\ln[\Gamma(x + 1)]$, $\Gamma$ being the usual Gamma function. The first one relies on an integral representation of
Externí odkaz:
http://arxiv.org/abs/2405.05264
Akademický článek
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Autor:
Pain, Jean-Christophe
In this note, we propose two series expansions of the logarithm of the Glaisher-Kinkelin constant. The relations are obtained using expressions of derivatives of the Riemann zeta function, and one of them involves hypergeometric functions.
Externí odkaz:
http://arxiv.org/abs/2304.07629
Autor:
Beltraminelli, Stefano1, Merlini, Danilo1,2,3 merlini@cerfim.ch, Sala, Massimo2,3, Sala, Nicoletta2,3,4 nicolettasalavb@gmail.com
Publikováno v:
Chaos & Complexity Letters. 2020, Vol. 14 Issue 3, p163-171. 9p.
Autor:
Wang, Weiping, Liu, Hongmei
Publikováno v:
In Applied Mathematics and Computation 20 June 2016 283:153-162
Autor:
Chen, Chao-Ping, Lin, Long
Publikováno v:
In Journal of Number Theory August 2013 133(8):2699-2705
Autor:
Aimin Xu
Publikováno v:
Journal of Number Theory. 163:255-266
Based on the Bell polynomials, Chen and Lin (2013) [9] obtained explicitly the coefficients a m ( m = 1 , 2 , … ) in the following asymptotic expansion related to the Glaisher–Kinkelin constant A: 1 1 2 2 ⋯ n n ∼ A ⋅ n n 2 2 + n 2 + 1 12 e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a7dffdc4566b06c8edfaa73528262c01
https://doi.org/10.1016/j.jnt.2015.11.010
https://doi.org/10.1016/j.jnt.2015.11.010
Autor:
Hongmei Liu, Weiping Wang
Publikováno v:
Applied Mathematics and Computation. 283:153-162
In this paper, by the Bernoulli numbers and the exponential complete Bell polynomials, we establish two general asymptotic expansions related to the hyperfactorial function and the Glaisher-Kinkelin constant, where the coefficients in the series of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::933f7588038b0f51b161cfacb4cd2cf8
https://doi.org/10.1016/j.amc.2016.02.027
https://doi.org/10.1016/j.amc.2016.02.027