Geodesic
Summation of slowly convergent series by the Gaussian type of quadratures and application to the calculation of the values of the Riemann zeta function
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 46 (2021) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

Beside a short account on the summation/integration methods for slowly convergent series $($Laplace transform method for numerical and trigonometric series and the method of contour integration over a rectangle$)$, a method based on a new transformation of the series to a weighted integral, with respect to the weight function \[t\mapsto w(t)=\frac{1}{qrt{t}\cosh^2\dfrac{iqrt{t}}{2}}\] over $\RR_+$, is presented. Such a method is applied to calculation of the values of the Riemann zeta function. Several numerical examples are included. 
@article{BASS_2021_46_1_a7,
     author = {Gradimir V. Milovanovi\'c},
     title = {Summation of slowly convergent series by the {Gaussian} type of quadratures and application to the calculation of the values of the {Riemann} zeta function},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {131 - 150},
     year = {2021},
     volume = {46},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BASS_2021_46_1_a7/}
}
TY  - JOUR
AU  - Gradimir V. Milovanović
TI  - Summation of slowly convergent series by the Gaussian type of quadratures and application to the calculation of the values of the Riemann zeta function
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2021
SP  - 131 
EP  -  150
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASS_2021_46_1_a7/
ID  - BASS_2021_46_1_a7
ER  - 
%0 Journal Article
%A Gradimir V. Milovanović
%T Summation of slowly convergent series by the Gaussian type of quadratures and application to the calculation of the values of the Riemann zeta function
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2021
%P 131 - 150
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2021_46_1_a7/
%F BASS_2021_46_1_a7
Gradimir V. Milovanović. Summation of slowly convergent series by the Gaussian type of quadratures and application to the calculation of the values of the Riemann zeta function. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 46 (2021) no. 1. http://geodesic.mathdoc.fr/item/BASS_2021_46_1_a7/