- #1
Pyroadept
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Homework Statement
Say f(z) = Σ(z^n), with sum from 0 to infinity
Then we can say f'(z) = Σn(z^n-1), with sum from 0 to infinity (i)
= Σn(z^n-1), with sum from 1 to infinity (as the zero-th term is 0)
= Σ(n+1)(z^n), with sum from 0 to infinity (ii)
Homework Equations
The Attempt at a Solution
Hi,
I am solving an ODE using power series, zf'(z) + af(z) = f'(z), so is it ok for me to sub in eq. (i) for the first f'(z) and eq. (ii) for the second? (This way all the terms will contain a z^n. Or is this cheating? If so, what can I do instead?)
Thanks for any help