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 TemplateBox[{{x, +, {i,  , y}}, {1, /, 2}}, QGamma]:

Plot the imaginary part of TemplateBox[{{x, +, {i,  , y}}, {1, /, 2}}, QGamma]:

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)