Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

Details Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

2012-02-09

arxiv.org/abs/1202.2006v1

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

In the paper, the author establishes some identities which show that the
functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm
t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with
coefficients involving the combinatorial numbers and the Stirling numbers of
the second kind, where $t\ne0$ and $i,k\in\mathbb{N}$.

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