I stumbled upon a problem that I'm not sure is stated correctly. They claim the following (without steps):
$$\sum_{m\geq 3} [4 \cdot \binom{\frac{1}{2}}{ m} + \binom{ \frac{1}{2}} {m-1}]\cdot\frac{x^m}{\Gamma(m - \frac{3}{2})}$$ $$=\frac{3e^{-x}(2 - 2e^x + xe^x + x)}{2\sqrt{\pi}}$$
Two questions: 1) is it actually possible to simplify this sum as stated? 2) is their answer actually correct?