On four families of power series involving harmonic numbers and central binomial coefficients

D. Romberger; H. J. Bentz; J. Braun

arxiv: 2006.13115 · v1 · pith:GQ4MNK6Anew · submitted 2020-06-23 · 🧮 math.NT

On four families of power series involving harmonic numbers and central binomial coefficients

J. Braun , D. Romberger , H. J. Bentz This is my paper

classification 🧮 math.NT

keywords harmonicnumbersbinomialcentralcoefficientsseriesfamiliesfunctions

0 comments

read the original abstract

We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate different families of power series which involve odd harmonic numbers and central binomial coefficients. Furthermore it is shown that based on these series a new type of nonlinear Euler sums that involve odd harmonic numbers can be calculated in terms of zeta functions.

This paper has not been read by Pith yet.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Evaluation of eight different families of cubic Euler sums
math.NT 2026-05 unverdicted novelty 5.0

All nonlinear cubic Euler sums in the eight families for degrees 4, 5, and 6 reduce to combinations of zeta functions and polylogarithms evaluated at 1/2, -1/2, and -1/8.