43 research outputs found
Simultaneous generation for zeta values by the Markov-WZ method
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 consequence, we get a new identity producing Ap\'ery-like series for all
convergent at the geometric rate with ratio
Comment: 7 page
Congruences concerning Jacobi polynomials and Ap\'ery-like formulae
Let be a prime. We prove congruences modulo for sums of the
general form and
with . We also consider the
special case of the former sum, where the congruences hold
modulo .Comment: to appear in Int. J. Number Theor
How to generate all possible rational Wilf-Zeilberger pairs?
A Wilf--Zeilberger pair in the discrete case satisfies the equation
. We present a structural
description of all possible rational Wilf--Zeilberger pairs and their
continuous and mixed analogues.Comment: 17 pages, add the notion of pseudo residues in the differential case,
and some related papers in the reference, ACMES special volume in the Fields
Institute Communications series, 201
Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums
We show some new Wolstenholme type q-congruences for some classes of multiple q-harmonic sums of arbitrary depth with strings of indices composed of ones, twos, and threes. Most of these results are q-extensions of the corresponding congruences for ordinary multiple harmonic sums obtained by the authors in a previous paper. We also establish duality congruences for multiple q-harmonic non-strict sums and a kind of duality for multiple q-harmonic strict sums. Finally, we pose a conjecture concerning two kinds of cyclic sums of multiple q-harmonic sums