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Template:Falling factorial/doc
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falling factorial}} mathematical function template returns the falling factorial
of the real number
,
being a nonnegative integer, otherwise returns an error message. This template works by repeating conditional multiplications.
for a real number
and a nonnegative integer
, otherwise returns an error message.
The {{(x)n |
x |
n |
Contents
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 |
x |
n |
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
- {{factorial}} or {{n!}}
- {{rising factorial}} or {{risefact}} or {{Pochhammer}} or {{Poch}} or {{x^(n)}}
- {{falling factorial}} or {{fallfact}} or {{(x)_n}}