is the generalized hypergeometric function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- has series expansion , where is the Pochhammer symbol.
- Hypergeometric0F1, Hypergeometric1F1, and Hypergeometric2F1 are special cases of HypergeometricPFQ.
- In many special cases, HypergeometricPFQ is automatically converted to other functions.
- For certain special arguments, HypergeometricPFQ automatically evaluates to exact values.
- HypergeometricPFQ can be evaluated to arbitrary numerical precision.
- For , HypergeometricPFQ[alist,blist,z] has a branch cut discontinuity in the complex plane running from to .
- FullSimplify and FunctionExpand include transformation rules for HypergeometricPFQ.
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (4)
Plot the HypergeometricPFQ function:
Function Properties (2)
Domain of HypergeometricPFQ:
Series Expansions (4)
Fractional derivative of Sin:
Derivative of order of Sin:
Plot a smooth transition between the derivative and integral of Sin: