Closed form expressions for some series over certain trigonometric integrals

Abstract

The series (3) and (4), where T(x) denotes trigonometric integrals (2), are represented as series in terms of Riemann zeta and related functions using the sums of the series (5) and (6), whose terms involve one trigonometric function. These series can be brought in closed form in some cases, where closed form means that the series are represented by finite sums of certain integrals. By specifying the function φ(y) appearing in trigonometric integrals (2) we obtain new series for some special types of functions as well as known results.

Keywords:

• Bessel functions
• Riemann zeta and related functions

AMS Classification:

• 44A15
• 33C40

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^bDepartment of Mathematics, Faculty of Civil Engineering, University of Niš, Beogradska 14, 18000 Niš Yugoslavia

^*Corresponding author. [email protected]

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^bDepartment of Mathematics, Faculty of Civil Engineering, University of Niš, Beogradska 14, 18000 Niš Yugoslavia

^*Corresponding author. [email protected]

Notes

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^aDepartment of Mathematics, Faculty of Environmental Engineering, University of Niš, Čarnojevića 10a, 18000 Niš, Yugoslavia

^bDepartment of Mathematics, Faculty of Civil Engineering, University of Niš, Beogradska 14, 18000 Niš Yugoslavia

^*Corresponding author. [email protected]

Additional information

Notes on contributors

Slobodan B. Tričković

b *