QGamma

QGamma[z,q]

gives the -gamma function .

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
for .
for .
QGamma automatically threads over lists.

Examples

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Basic Examples (3)

Evaluate numerically:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Scope (17)

Numerical Evaluation (4)

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:

Specific Values (5)

Values at fixed points:

QGamma has a singularity at x=0:

Evaluate for symbolic x at integer and half-integer parameters:

Evaluate for symbolic q at integer and half-integer parameters:

Find a value of x for which QGamma[x,2]=10:

Visualization (3)

Plot the QGamma function:

Plot the QGamma as a function of its second parameter q:

Plot the real part of :

Plot the imaginary part of :

Function Properties (3)

The real domain of QGamma:

The complex domain:

QGamma threads elementwise over lists:

TraditionalForm formatting:

Differentiation (2)

The first derivative with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z when q=3:

Applications (1)

–deformation of :

Properties & Relations (1)

QGamma does not automatically produce polynomial symbolic answers; use FunctionExpand:

Introduced in 2008

(7.0)

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