Closed formulas for computing higher-order derivatives of functions involving exponential functions

Ai-Min Xu and Zhong-Di Cen

Applied Mathematics and Computation, 2015, vol. 270, issue C, 136-141

Abstract: For integers k ≥ 1 and n ≥ 0, the functions 1/(1−λeαt)k and the derivatives (1/(1−λeαt))(n) can be expressed each other by linear combinations. Based on this viewpoint, we find several new closed formulas for higher-order derivatives of trigonometric and hyperbolic functions, derive a higher-order convolution formula for the tangent numbers, and generalize a recurrence relation for the tangent numbers.

Keywords: Closed formula; Higher-order derivative; Trigonometric function; Hyperbolic function; Tangent number (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:136-141

DOI: 10.1016/j.amc.2015.08.051

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