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Template:~(/doc

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[⧼Purge⧽ Template:~(/doc]

The {{~(|expression to delimit|)~}} mathematical formatting template delimits expressions with normal or larger size curly brackets (braces) for either HTML+CSS or LaTeX.

Note: neither a {{[|...|]}} (square bracket) template nor a {{{|...|}}} (brace) template works with MediaWiki!

Usage

{{~(|expression to delimit|)~}}

or

{{~(|expression to delimit|)~|type}}

or

{{~(|expression to delimit|)~|format}}

or

{{~(|expression to delimit|)~|type|format}}

where the mandatory [dummy] second argument must be )~ for visual balancing of left and right delimiters, viz.

{{~(|expression to delimit|)~}}

and the [optional] third argument (type) is from

• default: normal { ... }, corresponds to \{ ... \} in LaTeX;
• big: corresponds to \big\{ ... \big\} in LaTeX;
• Big: corresponds to \Big\{ ... \Big\} in LaTeX;
• bigg: corresponds to \bigg\{ ... \bigg\} in LaTeX;
• Bigg: corresponds to \Bigg\{ ... \Bigg\} in LaTeX;
• auto: corresponds to \left\{ ... \right\} in LaTeX;

and the [optional] format (either fourth argument, or third argument if type is omitted) is from

• htm: HTML+CSS (default);
• tex: LaTeX.

Examples

The code

A065918: Logarithm of {{math|2 + {{sqrt|3}}|tex = 2 + \sqrt{3}|&}}.

{{SoD's t or c| 1.3169578969248... }}

This number figures in the search for [[Mersenne primes]] thus: the [[Mersenne numbers|Mersenne number]] {{math|''M'' {{=}} 2{{^|''n''}} {{op|-}} 1|tex = M = 2^n - 1|&}} is [[prime]] if and only if {{math|''M''|tex = M|&}} divides{{nl|2}}

{{indent}}{{math|
{{begin|align}}
cosh{{sp|1}}(2{{^|''n''{{sp|1}}{{op|-}}2}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}}))
{{&=}} {{frac|''e''{{^|{{op|+}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2|87%}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})|)~}}}} +
''e''{{^|{{op|-}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2|87%}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})|)~}}}}|2|HTM}} {{\\}}
{{&=}} {{frac|(2 + {{sqrt|3}}{{sp|1}}){{^|{{op|+}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2{{sp|1}}|87%}}|)~}}}} +
(2 + {{sqrt|3}}{{sp|1}}){{^|{{op|-}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2{{sp|1}}|87%}}|)~}}}}|2|HTM}}{{sp|1}},
{{end|align}}
|tex =
\begin{align}
\cosh(2^{n-2} \log(2 + \sqrt{3}))
&= \frac{ e^{ + \{ 2^{n-2} \log(2 + \sqrt{3}) \} } + e^{ - \{ 2^{n-2} \log(2 + \sqrt{3}) \} } }{2} \\
&= \frac{ (2 + \sqrt{3})^{ + \{ 2^{n-2} \} } + (2 + \sqrt{3})^{ - \{ 2^{n-2} \} } }{2},
\end{align}
|&&}}{{clear}}

where {{math|cosh{{sp|1}}(''x'')|tex = \cosh(x)|&}} is the [[hyperbolic cosine]] function. {{User|David W. Wilson|David Wilson}} has proposed calling the number {{math|log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})
|tex = \log(2 + \sqrt{3})|&}} the [[Helms constant]].{{nl}}

The number {{math|2 + {{sqrt|3}} {{=}} tan {{tfrac|5{{sp|1}}{{Gr|pi}}|12}} {{=}} cot {{tfrac|{{Gr|pi}}|12}}|tex = 2 + \sqrt{3} = \tan \frac{5 \pi}{12} = \cot \frac{\pi}{12}|&}} is sometimes called the [[Kasner constant]] (see A019973 for decimal expansion).


yields

A065918: Logarithm of
 2 + 2√  3
.
1.3169578969248...
This number figures in the search for Mersenne primes thus: the Mersenne number
 M = 2 n  −  1
is prime if and only if
 M
divides

cosh (2n  − 2 log (2 +
2  3
))
=
 e  + { 2 n  − 2 log (2 + 2√  3 ) } + e  − { 2 n  − 2 log (2 + 2√  3 ) } 2
=
 (2 + 2√  3 )  + { 2 n  − 2  } + (2 + 2√  3 )  − { 2 n  − 2  } 2
,

where
 cosh (x)
is the hyperbolic cosine function. David Wilson has proposed calling the number
 log (2 + 2√  3 )
the Helms constant.
The number
2 +
2  3
= tan
 5 π 12
= cot
 π 12
is sometimes called the Kasner constant (see A019973 for decimal expansion).

Nonmathematical examples

The code

{{indent}}{{math|
{{~(|
{{begin|align}}
First: {{&}} 1
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}
First: {{&}} 1 {{\\}}
Second: {{&}} 1, 2
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}
First: {{&}} 1 {{\\}}
Second: {{&}} 1, 2 {{\\}}
Third: {{&}} 1, 2, 3 {{\\}}
Fourth: {{&}} 1, 2, 3, 4
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}
First: {{&}} 1 {{\\}}
Second: {{&}} 1, 2 {{\\}}
Third: {{&}} 1, 2, 3 {{\\}}
Fourth: {{&}} 1, 2, 3, 4 {{\\}}
Fifth: {{&}} 1, 2, 3, 4, 5 {{\\}}
Sixth: {{&}} 1, 2, 3, 4, 5, 6
{{end|align}}
|)~|auto}}
|&&}}


yields the display style HTML+CSS

 First: 1

 First: 1 Second: 1, 2

 First: 1 Second: 1, 2 Third: 1, 2, 3 Fourth: 1, 2, 3, 4

 First: 1 Second: 1, 2 Third: 1, 2, 3 Fourth: 1, 2, 3, 4 Fifth: 1, 2, 3, 4, 5 Sixth: 1, 2, 3, 4, 5, 6

The code

{{indent}}{{math|
{{~(|
{{begin|align|tex}}
\text{First:} {{&|tex}}\text{ 1}
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}
\text{Second:} {{&|tex}}\text{ 1, 2}
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}
\text{Second:} {{&|tex}}\text{ 1, 2} {{\\|tex}}
\text{Third:} {{&|tex}}\text{ 1, 2, 3} {{\\|tex}}
\text{Fourth:} {{&|tex}}\text{ 1, 2, 3, 4}
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}
\text{Second:} {{&|tex}}\text{ 1, 2} {{\\|tex}}
\text{Third:} {{&|tex}}\text{ 1, 2, 3} {{\\|tex}}
\text{Fourth:} {{&|tex}}\text{ 1, 2, 3, 4} {{\\|tex}}
\text{Fifth:} {{&|tex}}\text{ 1, 2, 3, 4, 5} {{\\|tex}}
\text{Sixth:} {{&|tex}}\text{ 1, 2, 3, 4, 5, 6}
{{end|align|tex}}
|)~|auto|tex}}
|}}


yields the display style LaTeX

{\displaystyle {\begin{array}{l}\displaystyle {\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\\{\text{Third:}}&{\text{ 1, 2, 3}}\\{\text{Fourth:}}&{\text{ 1, 2, 3, 4}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\\{\text{Third:}}&{\text{ 1, 2, 3}}\\{\text{Fourth:}}&{\text{ 1, 2, 3, 4}}\\{\text{Fifth:}}&{\text{ 1, 2, 3, 4, 5}}\\{\text{Sixth:}}&{\text{ 1, 2, 3, 4, 5, 6}}\end{aligned}}\right\}}\end{array}}}