Following a suggestion from this thread on Computational Science, I had a brief look at a plot of $$ f(E) = \frac{U(-E,1,R)}{\Gamma(1+E)}, $$ i.e. the Tricomi confluent hypergeometric function as a function of its first parameter, which looks like this

for $R=10$. I'm struck by the resemblance to an Airy function, but I can't find any clean results relating the two. Are any such links known?