An interplay between a generalized-Euler-constant function and the Hurwitz zeta function
Lampret, Vito
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 741-747 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2010-08-15
Classification:  estimate,  generalized-Euler-constant function,  Hurwitz-zeta function,  11Y60,  40A05,  40A25 
@article{1290608199,
     author = {Lampret, Vito},
     title = {An interplay between a generalized-Euler-constant function
and the Hurwitz zeta function},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 741-747},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1290608199}
}

Lampret, Vito. An interplay between a generalized-Euler-constant function
and the Hurwitz zeta function. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  741-747. http://gdmltest.u-ga.fr/item/1290608199/