On the higher derivatives of the inverse tangent function

Authors : Mohamed Amine BOUTICHE, Mourad RAHMANI

Pages : 2643-2656

View : 12 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

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 $\arctaninsert ignore into journalissuearticles values(x);$. 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