Hey schreckenstat.
What is F^i(x) referring to? Are these derivatives of some kind?
I've been working on a homework problem for an enumeration course that has been giving me fits.
Find a formula for f(n) if .
Can anyone explain how I can find a power series representation of F(x) from which I can find f(n)?
Thanks.
Sorry, I probably should've been a bit more descriptive in my first post. would be the function to the ith power. Generally in these sort of problems you solve for the generating function F(x), and then find a power series representation for F(x) from which you can construct another formula f(n) which would solve a recurrence relation. An easier example might be something like if , using the first two formulas in the first post we would have . In this case you could use the quadratic equation to find an expression for F(x), and then find a power series representation of F(x) to find f(n). The problem I'm having with this one is that I'm not sure how to attack that sum of sines to find an expression for F(x). Hope that makes things a bit more clear.