Template:Sinc

The following documentation is located at Template:Sinc/doc. [<Edit> Template:Sinc/doc]
[⧼Purge⧽ Template:Sinc]

The {{sinc}} mathematical function template returns either the normalized sinc function (default) or the unnormalized sinc function of a real number $\scriptstyle x\,$.

Usage

To get the normalized sinc function use

{{sinc|a real number}}

or

{{sinc|a real number|n}}.

To get the unnormalized sinc function use

{{sinc|a real number|u}}.

Valid input

A real number as first argument, n (normalized, default value) or u (unnormalized) as second argument.

Examples

Examples with valid input

Code	Result	Comment
{{sinc|-5/2|N}}	0.12732395447352
{{sinc|-2|n}}	-3.8981718325194E-17	(should be 0)
{{sinc|-1}}	3.8981718325194E-17	(should be 0)
{{sinc|-1/2}}	0.63661977236758
{{sinc|-1/3}}	0.82699334313269
{{sinc|-1/4}}	0.90031631615711
{{sinc|-1/6}}	0.95492965855137
{{sinc|0}}	1
{{sinc|1/6}}	0.95492965855137
{{sinc|1/4}}	0.90031631615711
{{sinc|1/3}}	0.82699334313269
{{sinc|1/2}}	0.63661977236758
{{sinc|1}}	3.8981718325194E-17	(should be 0)
{{sinc|2}}	-3.8981718325194E-17	(should be 0)
{{sinc|5/2}}	0.12732395447352

Code	Result	Comment
{{sinc|-5*pi/2|U}}	0.12732395447352
{{sinc|-2*pi|u}}	-3.8981718325194E-17	(should be 0)
{{sinc|-pi|u}}	3.8981718325194E-17	(should be 0)
{{sinc|-pi/2|u}}	0.63661977236758
{{sinc|-pi/3|u}}	0.82699334313269
{{sinc|-pi/4|u}}	0.90031631615711
{{sinc|-pi/6|u}}	0.95492965855137
{{sinc|0|u}}	1
{{sinc|pi/6|u}}	0.95492965855137
{{sinc|pi/4|u}}	0.90031631615711
{{sinc|pi/3|u}}	0.82699334313269
{{sinc|pi/2|u}}	0.63661977236758
{{sinc|pi|u}}	3.8981718325194E-17	(should be 0)
{{sinc|2*pi|u}}	-3.8981718325194E-17	(should be 0)
{{sinc|5*pi/2|u}}	0.12732395447352

Examples with invalid input (returns an error message)

Code	Result
{{sinc|i}}
{{sinc|0|pi}}

Code

{{#switch: {{lc: {{{2|n}}} }}  
| n = <!-- normalized --> 
  {{ifnum| {{{1|NAN}}}
  | {{#ifexpr: ({{{1}}}) = 0
    | 1
    | {{#expr: (sin (pi * ({{{1}}}) )) / (pi * ({{{1}}}) ) }}
    }}
  | {{error| Sinc error: First argument must be a real number }}
  }}
| u = <!-- unnormalized -->
  {{ifnum| {{{1|NAN}}}
  | {{#ifexpr: ({{{1}}}) = 0
    | 1
    | {{#expr: (sin ({{{1}}}) ) / ({{{1}}}) }}
    }}
  | {{error| Sinc error: First argument must be a real number }}
  }} 
| {{error| Sinc error: Second argument must be either n (normalized) or u (unnormalized) }}
}}