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:

HypergeometricPFQRegularized can be used with Interval and CenteredInterval objects:

Compute the elementwise values of an array:

Or compute the matrix HypergeometricPFQRegularized function using MatrixFunction:

For simple parameters, HypergeometricPFQRegularized evaluates to simpler functions:

Evaluate symbolically:

Value at zero:

Find a value of for which HypergeometricPFQRegularized[{2,1},{2,3},x]1.5:

Plot the HypergeometricPFQRegularized function for various parameters:

Plot the real part of :

Plot the imaginary part of :

HypergeometricPFQRegularized is defined for all real and complex values:

HypergeometricPFQRegularized threads elementwise over lists in its third argument:

HypergeometricPFQRegularized is an analytic function of z for specific values:

HypergeometricPFQRegularized is neither non-decreasing nor non-increasing for specific values:

HypergeometricPFQRegularized[{1,1,1},{3,3,3},z] is injective:

HypergeometricPFQRegularized[{1,1,1},{3,3,3},z] is not surjective:

HypergeometricPFQRegularized is neither non-negative nor non-positive:

HypergeometricPFQRegularized[{1,1,2},{3,3},z] has both singularity and discontinuity for z≥1 and at zero:

HypergeometricPFQRegularized is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to :

Higher derivatives with respect to :

Plot the higher derivatives with respect to when and :

Formula for the derivative with respect to z when a₁=1,a₂=2 and b₁=b₂=b₃=3:

Compute the indefinite integral using Integrate:

Verify the antiderivative:

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:

Find the series expansion at Infinity:

Find the series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: