Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate HypergeometricU efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix HypergeometricU function using MatrixFunction:

HypergeometricU automatically evaluates to simpler functions for certain parameters:

Limiting value at infinity:

Find a value of satisfying the equation :

Plot the HypergeometricU function:

Plot HypergeometricU as a function of its second parameter:

Plot the real part of :

Plot the imaginary part of :

Real domain of HypergeometricU:

Complex domain of HypergeometricU:

is not an analytic function:

is neither non-decreasing nor non-increasing on its real domain:

is injective:

is not surjective:

is positive on its real domain:

has both singularity and discontinuity for z≤0:

is convex on its real domain:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot higher derivatives for and :

Formula for the derivative:

Indefinite integral HypergeometricU:

Definite integral of HypergeometricU:

More integrals:

Series expansion for HypergeometricU:

Plot the first three approximations for around :

Expand HypergeometricU in series around infinity:

Apply HypergeometricU to a power series:

Compute the Laplace transform using LaplaceTransform:

MellinTransform:

HankelTransform:

Argument simplification:

Recurrence identities:

Primary definition:

Representation through Gamma and Hypergeometric1F1:

HypergeometricU can be represented in terms of MeijerG:

HypergeometricU can be represented as a DifferentialRoot:

TraditionalForm formatting: