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november 2010 An interplay between a generalized-Euler-constant function and the Hurwitz zeta function
Vito Lampret
Bull. Belg. Math. Soc. Simon Stevin 17(4): 741-747 (november 2010). DOI: 10.36045/bbms/1290608199

Abstract

For the generalized-Euler-constant function \[ a\mapsto \gamma(a):=\underset{n\rightarrow\infty}{\lim} \left(\sum_{i=0}^{n-1}\frac{1}{a+i}-\ln\frac{a+n-1}{a}\right) \] defined on $\R^+$, the expansion $\gamma(a)=\sum_{j=2}^{\infty}\frac{(-1)^j}{j}\,\zeta(j,a)$, where $\zeta(j,a)$ is the Hurwitz zeta function, is derived and a formula for its numerical computation is presented.

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Vito Lampret. "An interplay between a generalized-Euler-constant function and the Hurwitz zeta function." Bull. Belg. Math. Soc. Simon Stevin 17 (4) 741 - 747, november 2010. https://doi.org/10.36045/bbms/1290608199

Information

Published: november 2010
First available in Project Euclid: 24 November 2010

zbMATH: 1218.11081
MathSciNet: MR2778449
Digital Object Identifier: 10.36045/bbms/1290608199

Subjects:
Primary: 11Y60, 40A05, 40A25

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 4 • november 2010
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