Question

For a real number \(\alpha > 0 \) call \(\displaystyle \binom{\alpha}{n}:=\frac{\alpha(\alpha-1)(\alpha-2)...(\alpha+1-n)}{n!}\) the generalized binomial coeeficient. The products in the denominator and the numerator have \(n\) factors for each. Assume that \(\alpha \notin \mathbb{N}\)

b) Calculate Radius of convergence of the binomial series \(\sum_{n=0}^{\infty}\binom{\alpha}{n}x^{n}\)