Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler’s Constant
نویسندگان
چکیده
Let T be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over T , one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler’s constant, and study integrals over some polytopes that are higher-dimensional analogs of T . The latter leads to a relation between certain multiple polylogarithm values and multiple zeta values.
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