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.
Explicit formula, derivative polynomial, inverse tangent function, Chebyshev polynomial, matching polynomial
BOUTICHE, MOHAMED AMINE and RAHMANI, MOURAD
"On the higher derivatives of the inverse tangent function,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 41.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/41