81 citations · 142 across the 33 of their papers we have counts for
13 papers · 1 filter
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…
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…
Taylor coefficients of the Jacobi function
Tanay Wakhare, Christophe Vignat
We extend some results recently obtained by Dan Romik about the Taylor coefficients of the theta function to the case of an arbitrary va…
Identities for Bernoulli polynomials related to multiple Tornheim zeta functions
Karl Dilcher, Armin Straub, Christophe Vignat
We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order co…
Analytic Continuation for Multiple Zeta Values using Symbolic Representations
Lin Jiu, Tanay Wakhare, Christophe Vignat
We introduce a symbolic representation of -fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., suc…
A symbolic approach to the poly-Bernoulli numbers
T. Wakhare, C. Vignat
We present a symbolic representation for the poly-Bernoulli numbers. This allows us to prove several new iterated integral representations for the poly-Bernoulli numbers, including…