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arXiv · 1410.3014

Binomial transform and the backward difference

Khristo N. Boyadzhiev
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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.

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Khristo N. Boyadzhiev. 2014-10-11. Binomial transform and the backward difference. https://arxiv.org/abs/1410.3014

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