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arXiv · 0810.5077

Alternative evaluation of a ln tan integral arising in quantum field theory

Mark W. Coffey
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Abstract

A certain dilogarithmic integral I_7 turns up in a number of contexts including Feynman diagram calculations, volumes of tetrahedra in hyperbolic geometry, knot theory, and conjectured relations in analytic number theory. We provide an alternative explicit evaluation of a parameterized family of integrals containing this particular case. By invoking the Bloch-Wigner form of the dilogarithm function, we produce an equivalent result, giving a third evaluation of I_7. We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl_2.

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Mark W. Coffey. 2008-11-15. Alternative evaluation of a ln tan integral arising in quantum field theory. https://arxiv.org/abs/0810.5077

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