Related papers: A bivariate generating function for zeta values an…
Using the WZ method we present simpler proofs of Koecher's, Leshchiner's and Bailey-Borwein-Bradley's identities for generating functions of the sequences $\{\zeta(2n+2)\}_{n\ge 0}, \{\zeta(2n+3)\}_{n\ge 0}.$ By the same method we give…
In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting…
We document the discovery of two generating functions for the Riemann zeta values zeta(2n+2), analogous to earlier work for zeta(2n+1) and zeta(4n+3). This continues work initiated by Koecher and pursued further by Borwein, Bradley and…
By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Ap\'ery-like formulae for odd zeta values. As a…
Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for zeta(4n+3) which generalizes Apery's series for zeta(3), and appears to give the best possible series…
We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them have been long standing conjectures.
In this paper we formulate combinatorial identities that give representation of positive integers as linear combination of even powers of 2 with binomial coefficients. We present side by side combinatorial as well as computer generated…
It is known that the numbers which occur in Apery's proof of the irrationality of zeta(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove…
In the present paper, we prove an identity for the generating function of the quadruple zeta values. Taking homogeneous parts on both sides of the identity and substituting appropriate values for the variables, we obtain the sum formula for…
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for…
Through a systematic approach on generating Wilf-Zeilberger-pairs, we prove some hypergeometric identities conjectures due to Z.W. Sun, J. Guillera and Y. Zhao etc., including two Ramanujan-$1/\pi^4$, one $1/\pi^3$ formulas as well as a…
In this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler sums $\zeta\left(\overline{r}, s\right)$, $\zeta\left(r, \overline{s}\right)$…
This is the first of two papers in which we introduce and study two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. One of these zeta functions encodes the numbers of isomorphism…
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.
In this paper, we prove some supercongruences via the Wilf-Zeilberger method. For instance, for any odd prime $p$ and positive integer $r$ and $\delta\in\{1,2\}$, we have \begin{align*} \sum_{n=0}^{(p^r-1)/\delta}…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…
This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as…
In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…
We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results…