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 ...

Explore the profound connection between Euler's Identity and the Taylor series, two foundational concepts in mathematics. This overview explains how the expansion of exponential functions using the ...

We provide a proof of Euler’s sine product formula using simple techniques of calculus and illustrate how our method can be used to prove similar product formulas for cosine as well as hyperbolic sine ...