MODIFICATION EXPONENTIAL EULER TYPE SPLINES DERIVED FROM APOSTOL-EULER NUMBERS AND POLYNOMIALS OF COMPLEX ORDER.

The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers and polynomials of order with complex numbers with the aid of the Euler operator and partial derivatives of the generating function. Relations among the these numbers and polynomials of negative integer order, the beta-type rational functions, finite combinatorial sums, the Stirling numbers, and the Lah numbers are given. Finally, new classes of polynomials and modification exponential Euler type splines are constructed. [ABSTRACT FROM AUTHOR]