On the higher derivatives of the inverse tangent function

2017/12/10 by Boutiche, Mohamed Amine, Rahmani, Mourad
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.03521

Abstract

In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating functions, recurrence relations and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas and Matching polynomials are established.

Related

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• A family of two-variable derivative polynomials for tangent and secant