Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1712-40
Keywords
Explicit formula, derivative polynomial, inverse tangent function, Chebyshev polynomial, matching polynomial
First Page
2643
Last Page
2656
Recommended Citation
BOUTICHE, M. A, & RAHMANI, M (2018). On the higher derivatives of the inverse tangent function. Turkish Journal of Mathematics 42 (5): 2643-2656. https://doi.org/10.3906/mat-1712-40
