I'm very new to confluent hypergeometric functions so please bear with me. What I'm trying to prove is that $$M \left (\frac{c+m}{2m}, \frac{1}{2}, \frac{m}{2d}x^2 \right ) \rightarrow \infty \quad (1)$$ and $$U \left (\frac{c+m}{2m}, \frac{1}{2}, \frac{m}{2d}x^2 \right ) \rightarrow 0 \quad (2)$$ when $x \rightarrow \infty$. I know that's the case because I can compute their values, but I don't know how to show it.
I know from Abramowitz and Stegun's pocketbook that $M(a, b, z) = \frac{\Gamma(b)}{\Gamma(a)}e^z z^{a-b}[1+O(|z|^{-1})] $ when $|z| \rightarrow \infty$. $(1)$ is pretty clear from this because $a$ and $b$ are fixed. What about $(2)$?