About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

fresnels

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Compute the [Fresnel integral][fresnel-integral] S(x).

The [Fresnel integral][fresnel-integral] S(x) is defined as

$Fresnel integral S(x)$

Some sources define S(x) using t² for the argument of the sine. To get this function, multiply the computed integral by √(π/2) and multiply the argument x by √(2/π).

Installation

``bash npm install @stdlib/math-base-special-fresnels`

`Usage`

`javascript var fresnels = require( '@stdlib/math-base-special-fresnels' );`

#### fresnels( x )

Computes the [Fresnel integral][fresnel-integral] S(x).

`javascript var v = fresnels( 0.0 ); // returns ~0.0

v = fresnels( 1.0 ); // returns ~0.438

v = fresnels( Infinity ); // returns ~0.5

v = fresnels( -Infinity ); // returns ~-0.5

v = fresnels( NaN ); // returns NaN`

`Examples`

`javascript var linspace = require( '@stdlib/array-base-linspace' ); var fresnels = require( '@stdlib/math-base-special-fresnels' );

var x = linspace( 0.0, 10.0, 100 );

var i; for ( i = 0; i < x.length; i++ ) { console.log( fresnels( x[ i ] ) ); }`

*

`C APIs`

`$3`

`c #include "stdlib/math/base/special/fresnels.h"`

#### stdlib_base_fresnels( x )

Computes the [Fresnel integral][fresnel-integral] S(x).

`c double out = stdlib_base_fresnels( 0.0 ); // returns ~0.0

out = stdlib_base_fresnels( 1.0 ); // returns ~0.438`

The function accepts the following arguments:

- x: [in] double input value.

`c double stdlib_base_fresnels( const double x );`

`$3`

`c #include "stdlib/math/base/special/fresnels.h" #include

int main( void ) { const double x[] = { 0.0, 3.14, 5.55, 10.0 };

double y; int i; for ( i = 0; i < 4; i++ ) { y = stdlib_base_fresnels( x[ i ] ); printf( "fresnels(%lf) = %lf\n", x[ i ], y ); } }`

*

`Notice`

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-fresnels.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-fresnels

[test-image]: https://github.com/stdlib-js/math-base-special-fresnels/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/math-base-special-fresnels/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-fresnels/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-fresnels?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-fresnels/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-special-fresnels/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-special-fresnels/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-special-fresnels/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-special-fresnels/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-special-fresnels/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-special-fresnels/blob/main/branches.md

[fresnel-integral]: https://en.wikipedia.org/wiki/Fresnel_integral

[@stdlib/math/base/special/fresnel]: https://www.npmjs.com/package/@stdlib/math-base-special-fresnel

[@stdlib/math/base/special/fresnelc]: https://www.npmjs.com/package/@stdlib/math-base-special-fresnelc


  
    About stdlib...
  

  We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

  The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`fresnels`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Compute the [Fresnel integral][fresnel-integral] S(x).

The [Fresnel integral][fresnel-integral] S(x) is defined as

Some sources define S(x) using t² for the argument of the sine. To get this function, multiply the computed integral by √(π/2) and multiply the argument x by √(2/π).

`Installation`

``bash npm install @stdlib/math-base-special-fresnels `

`Usage`

`javascript var fresnels = require( '@stdlib/math-base-special-fresnels' ); `

#### fresnels( x )

Computes the [Fresnel integral][fresnel-integral] S(x).

`javascript var v = fresnels( 0.0 ); // returns ~0.0

v = fresnels( 1.0 ); // returns ~0.438

v = fresnels( Infinity ); // returns ~0.5

v = fresnels( -Infinity ); // returns ~-0.5

v = fresnels( NaN ); // returns NaN `

`Examples`

`javascript var linspace = require( '@stdlib/array-base-linspace' ); var fresnels = require( '@stdlib/math-base-special-fresnels' );

var x = linspace( 0.0, 10.0, 100 );

var i; for ( i = 0; i < x.length; i++ ) { console.log( fresnels( x[ i ] ) ); } `

*

`C APIs`

`$3`

`c #include "stdlib/math/base/special/fresnels.h" `

#### stdlib_base_fresnels( x )

Computes the [Fresnel integral][fresnel-integral] S(x).

`c double out = stdlib_base_fresnels( 0.0 ); // returns ~0.0

out = stdlib_base_fresnels( 1.0 ); // returns ~0.438 `

The function accepts the following arguments:

- x: [in] double input value.

`c double stdlib_base_fresnels( const double x ); `

`$3`

`c #include "stdlib/math/base/special/fresnels.h" #include

int main( void ) { const double x[] = { 0.0, 3.14, 5.55, 10.0 };

double y; int i; for ( i = 0; i < 4; i++ ) { y = stdlib_base_fresnels( x[ i ] ); printf( "fresnels(%lf) = %lf\n", x[ i ], y ); } } `

*

`Notice`

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-fresnels.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-fresnels

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-fresnels/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-fresnels?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[fresnel-integral]: https://en.wikipedia.org/wiki/Fresnel_integral

[@stdlib/math/base/special/fresnel]: https://www.npmjs.com/package/@stdlib/math-base-special-fresnel

[@stdlib/math/base/special/fresnelc]: https://www.npmjs.com/package/@stdlib/math-base-special-fresnelc

@stdlib/math-base-special-fresnels

fresnels

Installation

Usage

Examples

C APIs

$3

$3

See Also

Notice

Copyright

@stdlib/math-base-special-fresnels

fresnels

Installation

Usage

Examples

C APIs

$3

$3

See Also

Notice

Copyright

`Usage`

`Examples`

`C APIs`

`$3`

`$3`

`See Also`

`Notice`

`Copyright`

`@stdlib/math-base-special-fresnels`

`fresnels`

`Installation`

`Usage`

`Examples`

`C APIs`

`$3`

`$3`

`See Also`

`Notice`

`Copyright`