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.