Function Repository Resource:

# MultiFactorial

Evaluate the multifactorial function

Contributed by: Jan Mangaldan
 ResourceFunction["MultiFactorial"][n,k] gives the kth multifactorial of n.

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
For integer n, the kth multifactorial of nn!(k) is equal to n if 0<nk, and n ((n-k)!(k)) if k<n.
For certain special arguments, ResourceFunction["MultiFactorial"] automatically evaluates to exact values.
ResourceFunction["MultiFactorial"] can be evaluated to arbitrary numerical precision.
ResourceFunction["MultiFactorial"] automatically threads over lists.

## Examples

### Basic Examples (2)

Integer values:

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Evaluate numerically:

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### Scope (4)

Evaluate for large arguments:

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Evaluate at negative integers:

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Evaluate for complex arguments:

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MultiFactorial threads elementwise over lists:

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### Properties and Relations (2)

MultiFactorial[n,1] is equivalent to Factorial[n] (n!):

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MultiFactorial[n,2] is equivalent to Factorial2[n] (n!!):

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### Possible Issues (2)

Large arguments can give results too large to be computed explicitly, even approximately:

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Machine-number inputs can give arbitrary‐precision results:

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### Neat Examples (1)

Evaluate various reciprocal multifactorial constants:

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