Ueber eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechnung.

  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)},
  pages={122 - 138}
  • H. Kinkelin
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)

The Clausen function ${\sf Cl}_2(x)$ and its Related Integrals

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

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


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

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

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

  • Di YangJian Zhou
  • Mathematics
    Journal 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 $\zeta\left(\frac{1}{2}-it\right)\zeta'\left(\frac{1}{2}+it\right)$

. 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

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

New Approximations for the Higher Order Coefficients in an Asymptotic Expansion for the Barnes G-Function

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