Binomial transform and the backward difference
Number Theory
2017-02-03 v3
Abstract
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here are used to compute various binomial transform formulas involving harmonic numbers, skew-harmonic numbers, Fibonacci numbers, and Stirling numbers of the second kind. Several new identities are proved and some known results are given new short proofs.
Cite
@article{arxiv.1410.3014,
title = {Binomial transform and the backward difference},
author = {Khristo N. Boyadzhiev},
journal= {arXiv preprint arXiv:1410.3014},
year = {2017}
}
Comments
The paper is a slight modification of the journal article in Advances and Applications in Discrete Mathematics, 13 (1) (2014), 43-63