6 citations · 22 across the 25 of their papers we have counts for
14 papers · 1 filter
Tadpole Nahm sum as a Wronskian
Shane Chern, Chanh Tran, Tanay Wakhare
We show that the tadpole Nahm sum is essentially a specialization of a series studied by Bartlett and Warnaar. This overlooked connection was first discovered by the internal model…
A divisor generating -series and cumulants arising from random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +2
Uchimura, in 1987, introduced a probability generating function for a random variable and using properties of this function he discovered an interesting -series identity. He…
Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Parth Chavan, Sarth Chavan, Christophe Vignat +1
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its s…
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…
Romik's Conjecture for the Jacobi Theta Function
Tanay Wakhare
Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point . He then conjectured that the Taylor coefficients $d(…
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…
A Generalized Newton-Girard Identity
Tanay Wakhare
We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these ident…
Structural properties of multiple zeta values
Tanay Wakhare, Christophe Vignat
We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complemen…
Settling some sum suppositions
Tanay Wakhare, Christophe Vignat
We solve multiple conjectures by Byszewski and Ulas about the sum of base digits function. In order to do this, we develop general results about summations over the sum of digi…
Special values of -gamma products
Tanay Wakhare
We consider products of -gamma functions with rational arguments, and prove several -generalizations of recent works concerning products of gamma functions. In particular, we…
Finite generating functions for the sum of digits sequence
C. Vignat, T. Wakhare
We derive some new finite sums involving the sequence the sum of digits of the expansion of in base These functions allow us to generalize some clas…
Base- analogues of classic combinatorial objects
Tanay Wakhare, Christophe Vignat
We study the properties of the base- binomial coefficient defined by Jiu and the second author, introduced in the context of a digital binomial theorem. After introducing a gene…
A Continuous Analogue of Lattice Path Enumeration: Part II
T. Wakhare, C. Vignat
Here are exhibited some additional results about the continuous binomial coefficients as introduced by L. Cano and R. Diaz in [1].