New formulas of Euler's number e

Euler's number e(≒2.718281) is the base of a constant exponential function that does not change upon differentiation, and it is a very important constant frequently used in physical phenomena such as the motion of objects and electrical circuits. Since this number is an irrational number expressed in limits and infinite series, it is important to find formulas that converge more quickly to this number. This paper will discuss the function with the faster convergence to e and explain a new formula of e. Ultimately, I obtained new formulas of e.Furthermore, this paper proposes the introduction of imaginary numbers as a method to improve the convergence speed of even functions that converge to e.