On the higher derivatives of the inverse tangent function

Authors: MOHAMED AMINE BOUTICHE, MOURAD RAHMANI

Abstract: In this paper, we find explicit formulas for higher-order derivatives of the inverse tangent function. More precisely, we study polynomials that 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.

Keywords: Explicit formula, derivative polynomial, inverse tangent function, Chebyshev polynomial, matching polynomial

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