Title: On the higher derivatives of the inverse tangent function,
Abstract: In this paper, we find explicit formulas for higher order derivatives of the
inverse tangent function. More precisely, we study polynomials which 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.