Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem

DOI10.1007/s11075-008-9158-yzbMath1162.30025OpenAlexW1964064560MaRDI QIDQ1014746

Djurdje Cvijović, Hari M. Srivastava

Publication date: 29 April 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9158-y

zbMATH Keywords

Hurwitz zeta functionsintegral formulasCauchy integral theoremRiemann zeta functionscosecant integralssecant integrals

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Hurwitz and Lerch zeta functions (11M35) Zeta and (L)-functions: analytic theory (11M99) Exponential and trigonometric functions (33B10)

Cites Work

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• On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
• Certain classes of series involving the zeta function
• Closed-form evaluations of definite integrals and associated infinite series involving the Riemann zeta function
• Closed-form evaluation of some families of definite tangent and secant integrals

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