Evaluate to high precision:

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

Evaluate for complex arguments and parameters:

Evaluate Hypergeometric1F1 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 Hypergeometric1F1 function using MatrixFunction:

Hypergeometric1F1 automatically evaluates to simpler functions for certain parameters:

Limiting values at infinity for some case of Hypergeometric1F1:

Find a value of satisfying the equation :

Heun functions can be reduced to hypergeometric functions:

Plot the Hypergeometric1F1 function:

Plot Hypergeometric1F1 as a function of its second parameter:

Plot the real part of :

Plot the imaginary part of :

Real domain of Hypergeometric1F1:

Complex domain:

is an analytic function for real values of and :

For positive values of , it may or may not be analytic:

Hypergeometric1F1 is neither non-decreasing nor non-increasing except for special values:

is not injective:

is not surjective:

Hypergeometric1F1 is non-negative for specific values:

is neither non-negative nor non-positive:

has both singularity and discontinuity when is a negative integer:

is convex:

is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot higher derivatives for and :

Formula for the derivative:

Apply Integrate to Hypergeometric1F1:

Definite integral of Hypergeometric1F1:

More integrals:

Taylor expansion for Hypergeometric1F1:

Plot the first three approximations for around :

General term in the series expansion of Hypergeometric1F1:

Expand Hypergeometric1F1 in a series around infinity:

Apply Hypergeometric1F1 to a power series:

Compute the Laplace transform using LaplaceTransform:

HankelTransform:

Argument simplification:

Sum of the Hypergeometric1F1 functions:

Recurrence identity:

Primary definition:

Relation to the LaguerreL polynomial:

Hypergeometric1F1 can be represented as a DifferentialRoot:

Hypergeometric1F1 can be represented in terms of MeijerG: