4 research outputs found
A q-analogue of a formula of Hernandez obtained by inverting a result of Dilcher
We prove a q-analogue of the formula by inverting a formula due to Dilcher
Some -congruences for homogeneous and quasi-homogeneous multiple -harmonic sums
We show some new Wolstenholme type -congruences for some classes of
multiple -harmonic sums of arbitrary depth with strings of indices composed
of ones, twos and threes. Most of these results are -extensions of the
corresponding congruences for ordinary multiple harmonic sums obtained by the
authors in a previous paper. Finally, we pose a conjecture concerning two kinds
of cyclic sums of multiple -harmonic sums.Comment: This article is based on the previous version, but the results have
been reworked and extended substantiall
Ohno-type identities for multiple harmonic sums
We establish Ohno-type identities for multiple harmonic (-)sums which
generalize Hoffman's identity and Bradley's identity. Our result leads to a new
proof of the Ohno-type relation for -finite multiple zeta values
recently proved by Hirose, Imatomi, Murahara and Saito. As a further
application, we give certain sum formulas for - or
-finite multiple zeta values.Comment: 14 pages, Some minor correction
Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(a)
In this series of seven papers, predominantly by means of elementary
analysis, we establish a number of identities related to the Riemann zeta
function. Whilst this paper is mainly expository, some of the formulae reported
in it are believed to be new, and the paper may also be of interest
specifically due to the fact that most of the various identities have been
derived by elementary methods.Comment: This revised paper contains some corrections and some additional
materia