Ueber eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechnung.
@article{KinkelinUeberEM, title={Ueber eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechnung.}, author={Hermann Kinkelin}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, volume={1860}, pages={122 - 138} }
52 Citations
The Clausen function ${\sf Cl}_2(x)$ and its Related Integrals
- Mathematics
- 2014
The Clausen function ${\sf Cl}_2(x)$ arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of ${\sf…
On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
- Mathematics
- 2009
Abstract We discuss the asymptotic expansions of certain products of Bernoulli numbers and factorials, e.g., for integers k ≥ 1 and r ≥ 0. Our main interest is to determine exact expressions, in…
MATHEMATICAL CONSTANTS ASSOCIATED WITH THE MULTIPLE GAMMA FUNCTIONS
- Mathematics
- 2005
Abstract. The theory of multipleGamma functions was stud-ied in about 1900 and has, recently, been revived in the studyof determinants of Laplacians. There is a class of mathematicalconstants…
Statistics of Feynman amplitudes in $\phi^4$-theory
- Mathematics
- 2023
The amplitude of subdivergence-free logarithmically divergent Feynman graphs in $\phi^4$-theory in 4 spacetime dimensions is given by a single number, the Feynman period. We numerically compute the…
Series representations for the logarithm of the Glaisher-Kinkelin constant
- Mathematics
- 2023
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…
Grothendieck’s dessins d’enfants in a web of dualities. III
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2023
We give a new proof of the equivalence between the dessin partition function and the partition function of the Laguerre unitary ensemble (LUE), originally found by Ambjørn and Chekhov. We also…
Lambert series of logarithm, the derivative of Deninger's function $R(z)$ and a mean value theorem for $\zeta\left(\frac{1}{2}-it\right)\zeta'\left(\frac{1}{2}+it\right)$
- Mathematics
- 2022
. An explicit transformation for the series ∞ P n =1 log( n ) e ny − 1 , Re( y ) > 0, which takes y to 1 /y , is obtained for the first time. This series transforms into a series containing ψ 1 ( z ),…
H\"older and Kurokawa meet Borwein--Dykshoorn and Adamchik
- Mathematics
- 2022
Following our discovery of a nice identity in a recent preprint of Hu and Kim, we show a link between the Kurokawa multiple trigonometric functions and two functions introduced respectively by…
Several Results Concerning the Barnes G-function, a Cosecant Integral, and Some Other Special Functions
- Mathematics
- 2021
New Approximations for the Higher Order Coefficients in an Asymptotic Expansion for the Barnes G-Function
- MathematicsResults in Mathematics
- 2021
In this paper, we provide new formulas for determining the coefficients appearing in the asymptotic expansion for the Barnes G-function as n tends to infinity for certain classes of asymptotic…