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Template:Falling factorial

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The {{falling factorial}} mathematical function template returns the falling factorial
(x)n
of the real number
x
, 
n
being a nonnegative integer, otherwise returns an error message. This template works by repeating conditional multiplications.

Usage

{{falling factorial|real number x|nonnegative integer n}}

or

{{fallfact|real number x|nonnegative integer n}}

or

{{(x)_n|real number x|nonnegative integer n}}

Valid arguments

Returns 
(x)n
for a real number
x
and a nonnegative integer
n
, otherwise returns an error message.

Examples

Examples with valid argument

Code Result Code Result
{{falling factorial|1|0}} 1   {{fallfact|0|0}} 1
{{falling factorial|2|2}} 2   {{fallfact|0|1}} 0
{{falling factorial|3|3}} 6   {{fallfact|3|1}} 3
{{falling factorial|5|5}} 120   {{fallfact|5|3}} 60
{{falling factorial|10|10}} 3628800   {{fallfact|13|10}} 1037836800
{{falling factorial|16|16}} 20922789888000   {{fallfact|19|16}} 2.0274183401472E+16
{{(x)_n|3|0}} 1   {{(x)_n|3|3}} 6
{{(x)_n|3|1}} 3   {{(x)_n|10|3}} 720
{{(x)_n|3|2}} 6   {{(x)_n|16|3}} 3360
{{(x)_n|4|0}} 1   {{(x)_n|4|4}} 24
{{(x)_n|4|1}} 4   {{(x)_n|10|4}} 5040
{{(x)_n|4|2}} 12   {{(x)_n|16|4}} 43680
{{(x)_n|5|0}} 1   {{(x)_n|5|5}} 120
{{(x)_n|5|1}} 5   {{(x)_n|5|10}} 0
{{(x)_n|10|10}} 3628800   {{(x)_n|0|5}} 0
{{(x)_n|46|23}} 2.1285078898837E+35   {{(x)_n|57|5}} 502452720
{{(x)_n|89|10}} 1.8452514066426E+19   {{(x)_n|80|5}} 2884801920
{{(x)_n|-13|5}} -742560   {{(x)_n|0.5|3}} 0.375
{{(x)_n|2.71828|0}} 1   {{(x)_n|2.71828|5}} 1.2114144221281
{{(x)_n|-1.4142|0}} 1   {{(x)_n|-1.4142|5}} -278.58603191703
{{(x)_n|-2.4142|0}} 1   {{(x)_n|-2.4142|5}} -1263.5458392888
{{(x)_n|-3.4142|0}} 1   {{(x)_n|-3.4142|5}} -3880.4496568863

For maximum numbers allowed within {{expr}}, see{{Expr/doc#Maximum and minimum numbers allowed}}.

Examples with invalid argument (returns an error message)

Code Result
{{(x)_n|1|text}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|5|text}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|1|6 blobs}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|5|6 blobs}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|1|0.5}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|5|0.5}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|1|-1}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|5|-1}} Falling factorial error: Second argument must be a nonnegative integer
{{(x)_n|x|3}} Falling factorial error: First argument must be a number
{{(x)_n|5x|3}} Falling factorial error: First argument must be a number

See also