- #1

scorpion990

- 86

- 0

Of course, [tex]\frac{1}{\sqrt{1+x}} =\sum^{\infty}_{n=0} (\stackrel{-.5}{n})x^n [/tex].

However, this series doesn't converge for all x. It only converges if |x| < 1. In our case, [tex]|t^2 - 2xt|[/tex] would have to be less than 1.

In the derivation of many recursion formulas, powers of t are set equal to each other. However, this isn't valid for all values of t and x... How come this method of derivation is still valid? Any help/insight would be appreciated.