hi there... hope this is in the right place, even guidance to what the particular area of maths im talking about is would be appreciated, so I can find material/books online. thanks. where can I read about this?!

(I've only been learning about power series & generating functions for a week or 2..so this is probably a silly question)

I'm wondering if there's a generating function, and/or closed form (I think it's called) expression for the series z=z^2+c (ie as used in Mandelbrot set calculations).. ie a0=0, a1=c, a2=c^2+c, a3=(c^2+c)^2+c etc.... (z and c are complex)

ie I want to find the value of the nth term directly.

whether using a(n+1)=an^2+an-a(n-1)^2 is any better than a(n+1)=an^2+c, i have no idea... don't know if it's even possible.

also (how similar this question is, not sure..) the same calculation but just using real numbers - ie two sequences, where

X(n+1)=X(n)^2-Y(n)^2+a

Y(n+1)=2*X(n)*Y(n)+b

and X0=0, Y0=0, a+ib is the c from above.

ie generating functions & closed form expressions for these joined sequences, and pointers to where I could read about this sort of stuff! nothing I've found so far handles such series. thanks very much.