Template:Pochhammer/doc

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The {{Pochhammer}} mathematical function template returns the rising factorial (represented with

x (n)

or with the Pochhammer symbol

(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

{{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

Returns

x (n)

for a real number

x

and a nonnegative integer

n

, otherwise returns an error message.

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	Y	{{x^(n)|1|0}}	1	Y
{{Pochhammer|1|2}}	2	Y	{{x^(n)|1|2}}	2	Y
{{Pochhammer|1|3}}	6	Y	{{x^(n)|1|3}}	6	Y
{{Pochhammer|1|5}}	120	Y	{{x^(n)|1|5}}	120	Y
{{Pochhammer|1|10}}	3628800	Y	{{x^(n)|1|10}}	3628800	Y
{{Pochhammer|1|16}}	20922789888000	Y	{{x^(n)|1|16}}	20922789888000	Y
{{rising factorial|1|16}}	20922789888000	Y	{{risefact|1|16}}	20922789888000	Y
{{Poch|3|0}}	1	Y	{{Poch|3|3}}	60	Y
{{Poch|3|1}}	3	Y	{{Poch|3|10}}	239500800	Y
{{Poch|3|2}}	12	Y	{{Poch|3|16}}	3.201186852864E+15	Y
{{Poch|4|0}}	1	Y	{{Poch|4|4}}	840	Y
{{Poch|4|1}}	4	Y	{{Poch|4|10}}	1037836800	Y
{{Poch|4|2}}	20	Y	{{Poch|4|16}}	2.0274183401472E+16	Y
{{Poch|5|0}}	1	Y	{{Poch|5|5}}	15120	Y
{{Poch|5|1}}	5	Y	{{Poch|5|10}}	3632428800	Y
{{Poch|0|0}}	1	Y	{{Poch|0|5}}	0	Y
{{Poch|2.71828|0}}	1	Y	{{Poch|2.71828|5}}	1832.0760928814	Y
{{Poch|-1.4142|0}}	1	Y	{{Poch|-1.4142|5}}	1.4070633124019	Y
{{Poch|-2.4142|0}}	1	Y	{{Poch|-2.4142|5}}	-1.3136871563155	Y
{{Poch|-3.4142|0}}	1	Y	{{Poch|-3.4142|5}}	2.828345749207	Y

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}}
{{Poch|5|text}}
{{Poch|1|6 blobs}}
{{Poch|5|6 blobs}}
{{Poch|1|0.5}}
{{Poch|5|0.5}}
{{Poch|1|-1}}
{{Poch|5|-1}}
{{Poch|x|-1}}
{{Poch|5x|-1}}

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}}