# 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(23)

### 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(9)

The real domain of QGamma:

The complex domain:

is not an analytic function:

It has both singularities and discontinuities for and for :

is neither nonincreasing nor nondecreasing:

is not injective:

is not surjective:

is neither non-negative nor non-positive:

QGamma is neither convex nor concave:

### 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(2)

deformation of :

-series are building blocks of other -factorial functions:

## Properties & Relations(1)

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

Wolfram Research (2008), QGamma, Wolfram Language function, https://reference.wolfram.com/language/ref/QGamma.html.

#### Text

Wolfram Research (2008), QGamma, Wolfram Language function, https://reference.wolfram.com/language/ref/QGamma.html.

#### CMS

Wolfram Language. 2008. "QGamma." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/QGamma.html.

#### APA

Wolfram Language. (2008). QGamma. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QGamma.html

#### BibTeX

@misc{reference.wolfram_2024_qgamma, author="Wolfram Research", title="{QGamma}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/QGamma.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_qgamma, organization={Wolfram Research}, title={QGamma}, year={2008}, url={https://reference.wolfram.com/language/ref/QGamma.html}, note=[Accessed: 24-July-2024 ]}