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