93 lines
2.3 KiB
Markdown
93 lines
2.3 KiB
Markdown
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<!--
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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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# Apéry's Constant
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> [Apéry's constant][apery-constant].
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<section class="intro">
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[Apéry's constant][apery-constant] is defined as
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<!-- <equation class="equation" label="eq:apery_constant" align="center" raw="\zeta(3) = \sum_{n=1}^\infty \frac{1}{n^3} = \lim_{n\to\infty} \biggl(\frac{1}{1^3} + \frac{1}{2^3} + \cdots + \frac{1}{n^3}\biggr)" alt="Apéry's constant"> -->
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<div class="equation" align="center" data-raw-text="\zeta(3) = \sum_{n=1}^\infty \frac{1}{n^3} = \lim_{n\to\infty} \biggl(\frac{1}{1^3} + \frac{1}{2^3} + \cdots + \frac{1}{n^3}\biggr)" data-equation="eq:apery_constant">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float64/apery/docs/img/equation_apery_constant.svg" alt="Apéry's constant">
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<br>
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</div>
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<!-- </equation> -->
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where `ζ(s)` is the [Riemann zeta function][@stdlib/math/base/special/riemann-zeta]
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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 APERY = require( '@stdlib/constants/float64/apery' );
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```
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#### APERY
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[Apéry's constant][apery-constant].
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```javascript
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var bool = ( APERY === 1.2020569031595942 );
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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 APERY = require( '@stdlib/constants/float64/apery' );
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console.log( APERY );
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// => 1.2020569031595942
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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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[apery-constant]: https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant
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[@stdlib/math/base/special/riemann-zeta]: https://www.npmjs.com/package/@stdlib/math-base-special-riemann-zeta
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</section>
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<!-- /.links -->
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