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 ...

In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...

Description: Designed to provide algebraic concepts and skills including sets of real numbers, exponents, complex fractions, linear equations and quadratic equations, rectangular coordinates, ...

Figure 4. A snapshot, in time, of two complex numbers whose exponents, and thus their phase angles, change with time. The notion of negative frequency is often troubling to engineers who've spent so ...