Modified Apostol-Euler numbers and polynomials of higher order

M. G. Bin-Saad, A. Z. Bin-Alhag

The purpose of this work is to give modified definitions of Apostol-Euler polynomials and numbers of higher order. We establish their elementary properties, sums, explicit relations, integrals and differential relations. A number of new results which introduced are generalization of known results and their special cases lead to the corresponding formulas of the classical Euler numbers and polynomials.

Tbilisi Mathematical Journal, Vol. 11(4) (2018), 53-66