Evaluate to high precision:

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

Evaluate for complex arguments and parameters:

Evaluate Hypergeometric0F1 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 Hypergeometric0F1 function using MatrixFunction:

Evaluate symbolically for half-integer parameters:

Limiting value at infinity:

Find a zero of :

Heun functions can be reduced to hypergeometric functions:

Plot the Hypergeometric0F1 function for various values of parameter :

Plot Hypergeometric0F1 as a function of its first parameter :

Plot the real part of :

Plot the imaginary part of :

Real domain of :

Complex domain:

is an analytic function when :

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

is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

is surjective:

Note that the latter function grows very slowly as :

Hypergeometric0F1 is neither non-negative nor non-positive:

has no singularities or discontinuities:

is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Formula for the derivative:

Indefinite integral of Hypergeometric0F1:

Definite integral:

Integral involving a power function:

Taylor expansion for Hypergeometric0F1:

Plot the first three approximations for around :

General term in the series expansion of Hypergeometric0F1:

Series expansion for at infinity:

Product of the Hypergeometric0F1 functions:

Recurrence relation:

Use FunctionExpand to express Hypergeometric0F1 through other functions:

Series representation:

Relation to Hypergeometric1F1 function:

Hypergeometric0F1 can be represented as a DifferentialRoot:

Hypergeometric0F1 can be represented in terms of MeijerG:

TraditionalForm formatting: