Question:
Let F(z) be the antiderivative of f(z)=e^(z^2)with F(0). Find F(z) as a power series around z=0.
Attempt at solution:
We know that,
Hence,
Thus,
Now this is where i have problems, to find C,
let
Integrating we find,
Therefore,
Therefore,
Is my methodology correct? there is no answer in the book for some reason, but upon research i think my power series is correct, but none of them have a value for C when doing an indefinate integral.