hypergeometric_U( a , b , z )

The confluent hypergeometric function of the second kind of z in SageMath. The solution to the differential equation

$z \frac{d^2 f}{dz^2} + (b-z) \frac{df}{dz} - a z = 0$

that satisfies $$U(a,b,z) \sim x^{-a}$$ as $$x \rightarrow \infty$$.

Plot on the real axis: