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, MOHAMED AMINE and RAHMANI, MOURAD
(2018)
"On the higher derivatives of the inverse tangent function,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 41.
https://doi.org/10.3906/mat-1712-40
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/41
