104 lines
2.7 KiB
Markdown
104 lines
2.7 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Glaisher-Kinkelin Constant
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> [Glaisher-Kinkelin][glaisher-constant] constant.
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<section class="intro">
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[Glaisher-Kinkelin][glaisher-constant] constant is defined as
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<!-- <equation class="equation" label="eq:glaisher_kinkelin_constant" align="center" raw="A = \lim_{n\to\infty} \frac{K(n + 1)}{n^{n^2/2 + n/2 + 1/12}e^{-n^2/4}}" alt="Glaisher-Kinkelin constant"> -->
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<div class="equation" align="center" data-raw-text="A = \lim_{n\to\infty} \frac{K(n + 1)}{n^{n^2/2 + n/2 + 1/12}e^{-n^2/4}}" data-equation="eq:glaisher_kinkelin_constant">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float64/glaisher-kinkelin/docs/img/equation_glaisher_kinkelin_constant.svg" alt="Glaisher-Kinkelin constant">
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<br>
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</div>
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<!-- </equation> -->
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where
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<!-- <equation class="equation" label="eq:k_function" align="center" raw="K(n) = \prod_{k=1}^{n-1} k^k" alt="K-function"> -->
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<div class="equation" align="center" data-raw-text="K(n) = \prod_{k=1}^{n-1} k^k" data-equation="eq:k_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float64/glaisher-kinkelin/docs/img/equation_k_function.svg" alt="K-function">
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<br>
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</div>
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<!-- </equation> -->
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is the [K-function][k-function].
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var A = require( '@stdlib/constants/float64/glaisher-kinkelin' );
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```
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#### A
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The [Glaisher-Kinkelin][glaisher-constant] constant.
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```javascript
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var bool = ( A === 1.2824271291006226 );
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// returns true
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- TODO: better example -->
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<!-- eslint no-undef: "error" -->
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```javascript
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var A = require( '@stdlib/constants/float64/glaisher-kinkelin' );
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console.log( 'Glaisher\'s constant: %d', A );
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// => 'Glaisher\'s constant: 1.2824271291006226'
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[glaisher-constant]: https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant
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[k-function]: https://en.wikipedia.org/wiki/K-function
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</section>
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<!-- /.links -->
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