# Homework Help: Weird Generating Function prove

1. May 28, 2004

### phoenixy

Q: show that (1-4x)^(-1/2) generates the sequence 2n chooses n, n is defined as natural

All the formulas I have requires integer exponent. I am not sure how to deal with (-1/2).

Thanks for any input!!!

2. May 28, 2004

### Dr Transport

expand the function in a Taylor series

$$f(x) = f(0) + x\frac{df(x)}{dx}|_0 +\frac{x}{2!}\frac{d^{2}f(x)}{dx^{2}}|_0 + ...$$

$$\frac{1}{\sqrt{1-4x}}$$
as you normally would, for example the first derivative is $$\frac{2x}{(1-4x)^{3/2}}$$.