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Template:Pochhammer
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(Redirected from Template:Rising factorial)
The following documentation is located at Template:Pochhammer/doc. [<Edit> Template:Pochhammer/doc]
[⧼Purge⧽ Template:Pochhammer]
The {{Pochhammer}} mathematical function template returns the rising factorial (represented with [⧼Purge⧽ Template:Pochhammer]
x (n) |
(x)n |
x |
n |
Contents
Usage
- {{rising factorial|real number x|nonnegative integer n}}
or
- {{risefact|real number x|nonnegative integer n}}
or
- {{Pochhammer|real number x|nonnegative integer n}}
or
- {{Poch|real number x|nonnegative integer n}}
or
- {{x^(n)|real number x|nonnegative integer n}}
Valid input
Returnsx (n) |
x |
n |
Examples
Examples with valid input
Numerical results.— Daniel Forgues 00:30, 12 March 2018 (EDT) Code Result Comment Code Result Comment {{Pochhammer|1|0}} 1 {{x^(n)|1|0}} 1 {{Pochhammer|1|2}} 2 {{x^(n)|1|2}} 2 {{Pochhammer|1|3}} 6 {{x^(n)|1|3}} 6 {{Pochhammer|1|5}} 120 {{x^(n)|1|5}} 120 {{Pochhammer|1|10}} 3628800 {{x^(n)|1|10}} 3628800 {{Pochhammer|1|16}} 20922789888000 {{x^(n)|1|16}} 20922789888000 {{rising factorial|1|16}} 20922789888000 {{risefact|1|16}} 20922789888000 {{Poch|3|0}} 1 {{Poch|3|3}} 60 {{Poch|3|1}} 3 {{Poch|3|10}} 239500800 {{Poch|3|2}} 12 {{Poch|3|16}} 3.201186852864E+15 {{Poch|4|0}} 1 {{Poch|4|4}} 840 {{Poch|4|1}} 4 {{Poch|4|10}} 1037836800 {{Poch|4|2}} 20 {{Poch|4|16}} 2.0274183401472E+16 {{Poch|5|0}} 1 {{Poch|5|5}} 15120 {{Poch|5|1}} 5 {{Poch|5|10}} 3632428800 {{Poch|0|0}} 1 {{Poch|0|5}} 0 {{Poch|2.71828|0}} 1 {{Poch|2.71828|5}} 1832.0760928814 {{Poch|-1.4142|0}} 1 {{Poch|-1.4142|5}} 1.4070633124019 {{Poch|-2.4142|0}} 1 {{Poch|-2.4142|5}} -1.3136871563155 {{Poch|-3.4142|0}} 1 {{Poch|-3.4142|5}} 2.828345749207
For maximum numbers allowed within {{expr}}, see{{Expr/doc#Maximum and minimum numbers allowed}}.
Examples with invalid input (returns an error message)
Code Result {{Poch|1|text}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|5|text}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|1|6 blobs}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|5|6 blobs}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|1|0.5}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|5|0.5}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|1|-1}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|5|-1}} Pochhammer error: Second argument (number of iterations) must be a nonnegative integer within [0..32]. {{Poch|x|-1}} Pochhammer error: First argument (initial number) must be a real number. {{Poch|5x|-1}} Pochhammer error: First argument (initial number) must be a real number.
Code
Cf. {{Pochhammer/code}}.
Test
Cf. {{Pochhammer/test}}.
See also
- {{factorial}} or {{n!}}
- {{rising factorial}} or {{risefact}} or {{Pochhammer}} or {{Poch}} or {{x^(n)}}
- {{falling factorial}} or {{fallfact}} or {{(x)_n}}
- {{derangements}} or {{subfactorial}} or {{subfact}} or {{!n}}
- {{arrangements}}
Notes
- ↑ Note: depending on the context, the Pochhammer symbol
, introduced by Leo August Pochhammer, may represent either the rising factorial or the falling factorial.(x)n