Apostol Type $\left( p,q\right) $-Frobenius-Euler Polynomials and Numbers

Ugur Duran, Mehmet Acikgoz

In the present paper, we introduce $\left( p,q\right) $-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover $\left( p,q\right) $-extensions of Carlitz's result [L. Carlitz, Mat. Mag. { 32} (1959), 247-260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett. { 17} (2004), 375-380].