Evaluate numerically:

Evaluate to high precision:

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

Complex number inputs:

Evaluate 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 Hypergeometric1F1Regularized function using MatrixFunction:

Hypergeometric1F1Regularized for symbolic a:

Limiting values at infinity:

Values at zero:

Find a value of x for which Hypergeometric1F1Regularized[1/2,1,x ]=0.4:

Evaluate symbolically for integer parameters:

Evaluate symbolically for half-integer parameters:

Hypergeometric1F1Regularized automatically evaluates to simpler functions for certain parameters:

Plot the Hypergeometric1F1Regularized function:

Plot Hypergeometric1F1Regularized as a function of its second parameter :

Plot the real part of :

Plot the imaginary part of :

Hypergeometric1F1Regularized is defined for all real and complex values:

Hypergeometric1F1Regularized threads elementwise over lists:

is an analytic function:

Hypergeometric1F1Regularized is neither non-decreasing nor non-increasing except for special values:

is not injective:

is not surjective:

Hypergeometric1F1Regularized is non-negative for specific values:

is neither non-negative nor non-positive:

has no singularities or discontinuities:

is convex:

is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to b when a=1:

First derivative with respect to z when a=1:

Higher derivatives with respect to b when a=1:

Higher derivatives with respect to z when a=1 and b=2:

Plot the higher derivatives with respect to z when a=1 and b=2:

Formula for the derivative with respect to z when a=1:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

FourierSeries:

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point:

Recurrence relation:

Use FunctionExpand to express Hypergeometric1F1Regularized through other functions: