On some log-cosine integrals related to ζ(3), ζ(4), and ζ(6)

Authors:
Mark W. Coffey
Affiliations:
Department of Physics, Colorado School of Mines, Golden, CO
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 1
Cited 1

On some series containing &psgr; (x)—&psgr; (y)and 9 &psgr; (x)—&psgr; (y)2 for certain values of x and y

Journal of Computational and Applied Mathematics - Special volume on the occasion of the 65th birthday of Professor C. C. Grosjean

On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams

Journal of Computational and Applied Mathematics

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Abstract

We evaluate a variety of log-cosine integrals, one of which has value a rational multiple of πζ(4), while others evaluate to the form π[aζ(6) + b(3/4)ζ2(3)], where a 0 is rational and b is 1 or 2, and ζ is the Riemann zeta function. We show that these results may be obtained starting from a known tabulated result. The derivation yields results for certain classes of logarithm-trigonometric integrals, and indicates how further analytic results on digamma series may be obtained.