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LOG-SINE AND LOG-COSINE INTEGRALS

Choi, Junesang

  • Received : 2013.03.04
  • Accepted : 2013.03.28
  • Published : 2013.06.25

Abstract

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

Keywords

Beta function;Gamma function;Log-sine and log-cosine integrals;Harmonic numbers;Generalized harmonic numbers;Odd harmonic numbers;Generalized odd harmonic numbers;Riemann Zeta function;Hurwitz (or generalized) Zeta function;Psi (or Digamma) function;Polygamma functions;Euler-Mascheroni constant

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