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Built-in Mathematica Symbol

HypergeometricPFQRegularized

HypergeometricPFQRegularized[{a₁, ..., a_p}, {b₁, ..., b_q}, z]
is the regularized generalized hypergeometric function

HypergeometricPFQRegularized is finite for all finite values of its arguments so long as .

For certain special arguments, HypergeometricPFQRegularized automatically evaluates to exact values.

Evaluate numerically:

Evaluate symbolically:

Series expansion at the origin:

Evaluate numerically:

Evaluate symbolically:

Series expansion at the origin:

Evaluate for complex arguments and parameters:

Evaluate to high precision:

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

HypergeometricPFQRegularized evaluates to simpler functions for certain parameters:

HypergeometricPFQRegularized threads element-wise over lists in its third argument:

Find a fractional derivative of BesselJ:

Integral of order

of BesselJ[0, z]:

Use FunctionExpand to express the input in terms of simpler functions: