- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- On the higher derivatives of the inverse tangent function
On the higher derivatives of the inverse tangent function
Authors : Mohamed Amine Boutiche, Mourad Rahmani
Pages : 2643-2656
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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