Geodesic
Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals
Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 373-384

Voir la notice de l'article provenant de la source Cambridge

DOI

The Hurwitz zeta function ζ(s, a) is defined by the series for 0 < a ≤ 1 and σ = Re(s) > 1, and can be continued analytically to the whole complex plane except for a simple pole at s = 1 with residue 1. The integral functions C(s, a) and S(s, a) are defined in terms of the Hurwitz zeta function as follows: Using integral representations of C(s, a) and S(s, a), we evaluate explicitly a class of improper integrals. For example if 0 < a < 1 we show that
DOI : 10.4153/CMB-1993-051-6
Mots-clés : 11M35, Hurwitz zeta function, integral representation, evaluation of improper integrals, recurrence relations 
Yue, Zhang Nan; Williams, Kenneth S. Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals. Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 373-384. doi: 10.4153/CMB-1993-051-6
@article{10_4153_CMB_1993_051_6,
     author = {Yue, Zhang Nan and Williams, Kenneth S.},
     title = {Application of the {Hurwitz} {Zeta} {Function} to the {Evaluation} of {Certain} {Integrals}},
     journal = {Canadian mathematical bulletin},
     pages = {373--384},
     year = {1993},
     volume = {36},
     number = {3},
     doi = {10.4153/CMB-1993-051-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-051-6/}
}
TY  - JOUR
AU  - Yue, Zhang Nan
AU  - Williams, Kenneth S.
TI  - Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 373
EP  - 384
VL  - 36
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-051-6/
DO  - 10.4153/CMB-1993-051-6
ID  - 10_4153_CMB_1993_051_6
ER  - 
%0 Journal Article
%A Yue, Zhang Nan
%A Williams, Kenneth S.
%T Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals
%J Canadian mathematical bulletin
%D 1993
%P 373-384
%V 36
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-051-6/
%R 10.4153/CMB-1993-051-6
%F 10_4153_CMB_1993_051_6

Cité par Sources :