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 Hypergeometric0F1Regularized function using MatrixFunction:

Hypergeometric0F1Regularized for symbolic a:

Limiting value at infinity:

Values at zero:

Find a value of x for which Hypergeometric0F1Regularized[10,x ]=0.000001:

Evaluate symbolically for integer parameters:

Evaluate symbolically for half-integer parameters:

Plot the Hypergeometric0F1Regularized function for various values of parameter :

Plot Hypergeometric0F1Regularized as a function of its first parameter :

Plot the real part of :

Plot the imaginary part of :

is defined for all real and complex values:

Hypergeometric0F1Regularized threads elementwise over lists:

is an analytic function:

is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

is surjective:

Note that the latter function grows very slowly as :

Hypergeometric0F1Regularized is neither non-negative nor non-positive:

has no singularities or discontinuities:

is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to z when a=5/2:

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

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

Formula for the derivative with respect to z when a=1/2:

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 relations:

Use FunctionExpand to express Hypergeometric0F1Regularized through other functions: