Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function

Abstract

Using the Dirichlet integrals, which are employed in the theory of Fourier series, this paper develops a useful method for the summation of series and the evaluation of integrals.

References in corpus (6)

• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Some applications of the Stieltjes constants
• Some trigonometric integrals involving the log gamma and the digamma function
• Some integrals involving the Stieltjes constants:Part II
• Some applications of the sine and cosine integrals

Cited by in corpus (4)

• Some integrals and series involving the Stieltjes constants
• Fourier series and periodicity
• Some relations involving the higher derivatives of the Riemann zeta function
• On some new formulae involving the Stieltjes constants