If $E(z)= \sum _{n=0 }^{\infty }\frac {z ^n } {n! } $, how is $E(0) $ defined?

Question

If $E(z)= \sum _{n=0 }^{\infty }\frac {z ^n } {n! } $, how is $E(0) $ defined?

The exponential function for complex $z $ is defined in Rudin's principles as the power series $ \sum _{n=0 }^{\infty }\frac {z ^n } {n! } $, I cannot see that it is clear how this function is defined for $z=0 $. How is this typically done?

Thanks in advance!

Answer 1

$$E(z)=1+z+\frac{z^2}{2!}+\frac{z^3}{3!}+\cdots\\ E(0)=1+0/1+0^2/2+0^3/6\cdots=1$$