# QFactorial

QFactorial[n,q]

gives the -factorial .

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• for positive integer , and otherwise.
• QFactorial automatically threads over lists.

# Examples

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## Basic Examples(5)

Evaluate numerically:

Plot over a subset of the reals with respect to the first argument:

Plot over a subset of the reals with respect to q:

Plot over a subset of the complexes:

Series expansion at the origin:

Series expansion at Infinity:

## Scope(25)

### 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:

Value at zero:

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

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

Find a value of n for which QFactorial[n,2]=10:

### Visualization(3)

Plot the QFactorial function:

Plot the QFactorial 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 QFactorial:

The complex domain:

is not an analytic function:

It has both singularities and discontinuities for and :

is neither nonincreasing nor nondecreasing:

QFactorial is not injective:

QFactorial is not surjective:

is neither non-negative nor non-positive:

QFactorial is neither convex nor concave:

### Differentiation(2)

The first derivative with respect to n:

Higher derivatives with respect to n:

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

### Series Expansions(2)

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion at a generic point:

## Properties & Relations(1)

Use FunctionExpand to expand -series:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_qfactorial, author="Wolfram Research", title="{QFactorial}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/QFactorial.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_qfactorial, organization={Wolfram Research}, title={QFactorial}, year={2008}, url={https://reference.wolfram.com/language/ref/QFactorial.html}, note=[Accessed: 21-July-2024 ]}