Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers


Jiao-Lian Zhao - Department of Mathematics and Physics, Weinan Normal University, Weinan City, Shaanxi Province, 714009, China.
Jing-Lin Wang - Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China.
Feng Qi - Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.


In the paper, the authors find a simple and significant expression in terms of the Stirling numbers for derivative polynomials of a function with a parameter related to the higher order Apostol-Euler numbers and to the higher order Frobenius-Euler numbers. Moreover, the authors also present a common solution to a sequence of nonlinear ordinary differential equations.