Trigonometric integrals evaluated in terms of Riemann zeta and Dirichlet beta functions

Abstract

Three classes of trigonometric integrals involving an integer parameter are evaluated by the contour integration and the residue theorem. The resulting formulae are expressed in terms of Riemann zeta function and Dirichlet beta function. Several remarkable integral identities are presented.

Keywords

• cauchy residue theorem
• contour integration
• formal power series
• 30e20
• 11m32