105 lines
2.4 KiB
Markdown
105 lines
2.4 KiB
Markdown
|
<!--
|
||
|
|
|
||
|
|
@license Apache-2.0
|
||
|
|
|
||
|
|
Copyright (c) 2018 The Stdlib Authors.
|
||
|
|
|
||
|
|
Licensed under the Apache License, Version 2.0 (the "License");
|
||
|
|
you may not use this file except in compliance with the License.
|
||
|
|
You may obtain a copy of the License at
|
||
|
|
|
||
|
|
http://www.apache.org/licenses/LICENSE-2.0
|
||
|
|
|
||
|
|
Unless required by applicable law or agreed to in writing, software
|
||
|
|
distributed under the License is distributed on an "AS IS" BASIS,
|
||
|
|
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||
|
|
See the License for the specific language governing permissions and
|
||
|
|
limitations under the License.
|
||
|
|
|
||
|
|
-->
|
||
|
|
|
||
|
|
# j1
|
||
|
|
|
||
|
|
> Compute the [Bessel function of the first kind][bessel-first-kind] of order one.
|
||
|
|
|
||
|
|
<section class="intro">
|
||
|
|
|
||
|
|
The [Bessel function of the first kind][bessel-first-kind] of order one is defined as
|
||
|
|
|
||
|
|
<!-- <equation class="equation" label="eq:bessel_first_kind_order_one" align="center" raw="J_1 (x) = \frac{1}{2 \pi} \int_{-\pi}^\pi e^{i(\tau - x \sin(\tau))} \,d\tau" alt="Bessel function of the first kind of order one"> -->
|
||
|
|
|
||
|
|
<div class="equation" align="center" data-raw-text="J_1 (x) = \frac{1}{2 \pi} \int_{-\pi}^\pi e^{i(\tau - x \sin(\tau))} \,d\tau" data-equation="eq:bessel_first_kind_order_one">
|
||
|
|
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/besselj1/docs/img/equation_bessel_first_kind_order_one.svg" alt="Bessel function of the first kind of order one">
|
||
|
|
<br>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- </equation> -->
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.intro -->
|
||
|
|
|
||
|
|
<section class="usage">
|
||
|
|
|
||
|
|
## Usage
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var j1 = require( '@stdlib/math/base/special/besselj1' );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### j1( x )
|
||
|
|
|
||
|
|
Computes the [Bessel function of the first kind][bessel-first-kind] of order one at `x`.
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var v = j1( 0.0 );
|
||
|
|
// returns 0.0
|
||
|
|
|
||
|
|
v = j1( 1.0 );
|
||
|
|
// returns ~0.440
|
||
|
|
|
||
|
|
v = j1( Infinity );
|
||
|
|
// returns 0.0
|
||
|
|
|
||
|
|
v = j1( -Infinity );
|
||
|
|
// returns 0.0
|
||
|
|
|
||
|
|
v = j1( NaN );
|
||
|
|
// returns NaN
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.usage -->
|
||
|
|
|
||
|
|
<section class="examples">
|
||
|
|
|
||
|
|
## Examples
|
||
|
|
|
||
|
|
<!-- eslint no-undef: "error" -->
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var randu = require( '@stdlib/random/base/randu' );
|
||
|
|
var j1 = require( '@stdlib/math/base/special/besselj1' );
|
||
|
|
|
||
|
|
var x;
|
||
|
|
var i;
|
||
|
|
|
||
|
|
for ( i = 0; i < 100; i++ ) {
|
||
|
|
x = randu() * 10.0;
|
||
|
|
console.log( 'j1(%d) = %d', x, j1( x ) );
|
||
|
|
}
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.examples -->
|
||
|
|
|
||
|
|
<section class="links">
|
||
|
|
|
||
|
|
[bessel-first-kind]: https://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind:_J.CE.B1
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.links -->
|