Some applications of the Stieltjes constants

Abstract

In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of some integrals related to the Barnes multiple gamma functions.

References in corpus (3)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Theta and Riemann xi function representations from harmonic oscillator eigensolutions
• More Series related to the Euler Series

Cited by in corpus (8)

• Expansions of generalized Euler's constants into the series of polynomials in ${\pi }^{-2}$ and into the formal enveloping series with rational coefficients only
• On an integral involving the digamma function
• The difference between two Stieltjes constants
• Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function
• A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
• Some trigonometric integrals involving the log gamma and the digamma function
• Some integrals involving the Stieltjes constants:Part II
• Some applications of the sine and cosine integrals