Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals

The nth order derivatives of tan x and sec x may be represented by polynomials P _n (u) and Q _n (u) in u = tan x, which are known as the derivative polynomials for the tangent and secant and have occurred in diverse contexts. In this paper, explicit representations of P _n (u) and Q _n (u) are derived in terms of the central factorial numbers of the second kind, and the values of the Bernoulli and Euler polynomials at rationals are expressed by means of these polynomials.