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| 1 | +<!-- |
| 2 | +
|
| 3 | +@license Apache-2.0 |
| 4 | +
|
| 5 | +Copyright (c) 2025 The Stdlib Authors. |
| 6 | +
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| 7 | +Licensed under the Apache License, Version 2.0 (the "License"); |
| 8 | +you may not use this file except in compliance with the License. |
| 9 | +You may obtain a copy of the License at |
| 10 | +
|
| 11 | + http://www.apache.org/licenses/LICENSE-2.0 |
| 12 | +
|
| 13 | +Unless required by applicable law or agreed to in writing, software |
| 14 | +distributed under the License is distributed on an "AS IS" BASIS, |
| 15 | +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 16 | +See the License for the specific language governing permissions and |
| 17 | +limitations under the License. |
| 18 | +
|
| 19 | +--> |
| 20 | + |
| 21 | +# FLOAT32_APERY |
| 22 | + |
| 23 | +> [Apéry's constant][apery-constant]. |
| 24 | +
|
| 25 | +<section class="intro"> |
| 26 | + |
| 27 | +[Apéry's constant][apery-constant] is defined as |
| 28 | + |
| 29 | +<!-- <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"> --> |
| 30 | + |
| 31 | +```math |
| 32 | +\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) |
| 33 | +``` |
| 34 | + |
| 35 | +<!-- <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"> |
| 36 | + <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6e1cf583c4854b3d982f22f361f53a30c9f552dc/lib/node_modules/@stdlib/constants/float32/apery/docs/img/equation_apery_constant.svg" alt="Apéry's constant"> |
| 37 | + <br> |
| 38 | +</div> --> |
| 39 | + |
| 40 | +<!-- </equation> --> |
| 41 | + |
| 42 | +where `ζ(s)` is the [Riemann zeta function][@stdlib/math/base/special/riemann-zeta]. |
| 43 | + |
| 44 | +</section> |
| 45 | + |
| 46 | +<!-- /.intro --> |
| 47 | + |
| 48 | +<section class="usage"> |
| 49 | + |
| 50 | +## Usage |
| 51 | + |
| 52 | +```javascript |
| 53 | +var FLOAT32_APERY = require( '@stdlib/constants/float32/apery' ); |
| 54 | +``` |
| 55 | + |
| 56 | +#### FLOAT32_APERY |
| 57 | + |
| 58 | +[Apéry's constant][apery-constant]. |
| 59 | + |
| 60 | +```javascript |
| 61 | +var bool = ( FLOAT32_APERY === 1.202056884765625 ); |
| 62 | +// returns true |
| 63 | +``` |
| 64 | + |
| 65 | +</section> |
| 66 | + |
| 67 | +<!-- /.usage --> |
| 68 | + |
| 69 | +<section class="examples"> |
| 70 | + |
| 71 | +## Examples |
| 72 | + |
| 73 | +<!-- TODO: better example --> |
| 74 | + |
| 75 | +<!-- eslint no-undef: "error" --> |
| 76 | + |
| 77 | +```javascript |
| 78 | +var FLOAT32_APERY = require( '@stdlib/constants/float32/apery' ); |
| 79 | + |
| 80 | +console.log( FLOAT32_APERY ); |
| 81 | +// => 1.202056884765625 |
| 82 | +``` |
| 83 | + |
| 84 | +</section> |
| 85 | + |
| 86 | +<!-- /.examples --> |
| 87 | + |
| 88 | +<!-- C interface documentation. --> |
| 89 | + |
| 90 | +* * * |
| 91 | + |
| 92 | +<section class="c"> |
| 93 | + |
| 94 | +## C APIs |
| 95 | + |
| 96 | +<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --> |
| 97 | + |
| 98 | +<section class="intro"> |
| 99 | + |
| 100 | +</section> |
| 101 | + |
| 102 | +<!-- /.intro --> |
| 103 | + |
| 104 | +<!-- C usage documentation. --> |
| 105 | + |
| 106 | +<section class="usage"> |
| 107 | + |
| 108 | +### Usage |
| 109 | + |
| 110 | +```c |
| 111 | +#include "stdlib/constants/float32/apery.h" |
| 112 | +``` |
| 113 | + |
| 114 | +#### STDLIB_CONSTANT_FLOAT32_APERY |
| 115 | + |
| 116 | +Macro for [Apéry's constant][apery-constant]. |
| 117 | + |
| 118 | +</section> |
| 119 | + |
| 120 | +<!-- /.usage --> |
| 121 | + |
| 122 | +<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> |
| 123 | + |
| 124 | +<section class="notes"> |
| 125 | + |
| 126 | +</section> |
| 127 | + |
| 128 | +<!-- /.notes --> |
| 129 | + |
| 130 | +<!-- C API usage examples. --> |
| 131 | + |
| 132 | +<section class="examples"> |
| 133 | + |
| 134 | +</section> |
| 135 | + |
| 136 | +<!-- /.examples --> |
| 137 | + |
| 138 | +</section> |
| 139 | + |
| 140 | +<!-- /.c --> |
| 141 | + |
| 142 | +<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --> |
| 143 | + |
| 144 | +<section class="related"> |
| 145 | + |
| 146 | +</section> |
| 147 | + |
| 148 | +<!-- /.related --> |
| 149 | + |
| 150 | +<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> |
| 151 | + |
| 152 | +<section class="links"> |
| 153 | + |
| 154 | +[apery-constant]: https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant |
| 155 | + |
| 156 | +[@stdlib/math/base/special/riemann-zeta]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/riemann-zeta |
| 157 | + |
| 158 | +</section> |
| 159 | + |
| 160 | +<!-- /.links --> |
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