Derivative Polynomials for tanh, tan, sech and sec in Explicit Form

Abstract

The derivative polynomials for the hyperbolic and trigonometric tangent, cotangent and secant are found in explicit form, where the coefficients are given in terms of Stirling numbers of the second kind. As application, some integrals are evaluated and the reflection formula for the polygamma function is written in explicit form.

A similar version in The Fibonacci Quarterly, 2007

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