BIT Numerical Mathematics

, Volume 11, Issue 1, pp 21–28 | Cite as

On the value of a logarithmic-trigonometric integral

  • K. S. Kölbig


A closed expression is derived for the integral ∫ 0 π/2 log n cosxlog p sinxdx, wheren andp are non-negative integers. As already remarked by Nielsen in a monograph on the generalized polylogarithms published early in this century, this integral is equal to π times a homogeneous polynomial in σ(q) (the Riemann zeta function for integer arguments) and log 2, with rational coefficients. Explicit expressions for the integral are given for 0<n≦4, 0≦p≦4, most of which have been found from the general formula by means of a computer.


Computational Mathematic Explicit Expression General Formula Zeta Function Rational Coefficient 
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Copyright information

© BIT Foundations 1971

Authors and Affiliations

  • K. S. Kölbig
    • 1
  1. 1.CernGenevaSwitzerland

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