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.

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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. 
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     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},
     publisher = {mathdoc},
     volume = {46},
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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/