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 Hypergeometric2F1Regularized function using MatrixFunction:

Hypergeometric2F1Regularized for symbolic a and b:

Limiting values at infinity:

Values at zero:

Find a value of x for which Hypergeometric2F1Regularized[2,1,2,x ]=0.4:

Evaluate symbolically for integer parameters:

Evaluate symbolically for half-integer parameters:

Hypergeometric2F1Regularized automatically evaluates to simpler functions for certain parameters:

Plot the Hypergeometric2F1Regularized function:

Plot Hypergeometric2F1Regularized as a function of its second parameter :

Plot the real part of :

Plot the imaginary part of :

Real domain of Hypergeometric2F1Regularized:

Complex domain:

Recurrence identity:

Hypergeometric2F1Regularized threads elementwise over lists:

is analytic on its real domain:

It is neither analytic nor meromorphic in the complex plane:

is non-decreasing on its real domain:

is injective:

is not surjective:

is non-negative on its real domain:

has both singularity and discontinuity for :

is convex on its real domain:

TraditionalForm formatting:

First derivative with respect to z when a=1, b=2, c=3:

Higher derivatives with respect to z when a=1, b=1/2, c=1/3:

Plot the higher derivatives with respect to z when a=1, b=1/2, c=1/3:

Formula for the derivative with respect to z:

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 :

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: