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:

Series expansion about the origin:

Special values:

Related functions:   hypergeometric_M   hypergeometric

Function category: hypergeometric functions sagemath-docs