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A note on the higher derivatives of the function \(1/(\exp(x)-1)\). (English) Zbl 1357.26008
Summary: In this brief note, we compare two formulas for the higher order derivatives of the function \(1/(\exp(x)-1)\). We also provide an integral representation for these derivatives and obtain a classical formula relating zeta values and Bernoulli numbers.
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
11B68 Bernoulli and Euler numbers and polynomials
33B10 Exponential and trigonometric functions
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