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  (19)

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

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

Function Properties  (3)

The real domain of QFactorial:

The complex domain:

QFactorial threads elementwise over lists:

TraditionalForm formatting:

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:

Introduced in 2008
 (7.0)