204 citations
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7 papers · 1 filter
Alternative evaluation of a ln tan integral arising in quantum field theory
Mark W. Coffey
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 conject…
On a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions
Mark W. Coffey
Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. T…
Evaluation of a ln tan integral arising in quantum field theory
Mark W. Coffey
We analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new representations of the Clau…
Theta and Riemann xi function representations from harmonic oscillator eigensolutions
Mark W. Coffey
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations fo…
On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere
Mark W. Coffey
Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantu…
New results on the Stieltjes constants: Asymptotic and exact evaluation
Mark W. Coffey
The Stieltjes constants are the expansion coefficients in the Laurent series for the Hurwitz zeta function about s=1. We present new asymptotic, summatory, and other exact expressi…