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math.NT2020
On a result of Koecher concerning Markov-Apéry type formulas for the Riemann zeta function
Karl Dilcher, Christophe Vignat
Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for due to Markov and rediscov…
math.NT2020
A triple integral analog of a multiple zeta value
Tewodros Amdeberhan, Victor H. Moll, Armin Straub +1
We establish the triple integral evaluation \[ \int_{1}^{\infty} \int_{0}^{1} \int_{0}^{1} \frac{dz \, dy \, dx}{x(x+y)(x+y+z)} = \frac{5}{24} ζ(3), \] as well as the equivalent po…