Bateman Function

$$k_\nu(x) \equiv {e^{-x}\over \Gamma(1+{1\over 2}\nu)}U(-{\textstyle{1\over 2}}\nu,0,2x)$$

for $x>0$, where $U$ is a Confluent Hypergeometric Function of the Second Kind.

See also Confluent Hypergeometric Differential Equation, Hypergeometric Function