Exponential Series

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If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has a sum and we denote it by .If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has a sum and we denote it by .

It can also be proved that e^{x + y} = e^x.e^y for complex numbers x and y.

Theorem:

If x is a rational number, then the sum (e^x) of the exponential series