These three formulas are McLaughlin formula, in which McLaughlin formula is a special form of Taylor formula.

Replace x with ix in the expansion of e X.

So what?

So:? , and then add and subtract two formulas to get:?

,。 These two are also called Euler formulas. will

Take x in π and you get:

This identity, also known as Euler formula, is the most fascinating formula in mathematics, which connects several most important numbers in mathematics: two transcendental numbers: the base e, pi of natural logarithm; Two units: imaginary unit I and natural unit1;

And 0 is called one of the great discoveries of mankind. Mathematicians evaluate it as a "formula created by God".

Extended data:

On any positive spherical graph, if R is used to record the number of regions, V is used to record the number of vertices, and E is used to record the number of boundaries, then R+ V- E= 2, which is euler theorem? It was first proved by Descartes in 1640, and later independently proved by Euler in 1752. We call it euler theorem, and some people abroad call it Descartes theorem. ?

R+ V- E= 2 is Euler's formula.

References:

Baidu Encyclopedia-Euler Formula