The [inverse error function][inverse-error-function] is defined in terms of the [Maclaurin series][maclaurin-series] ```math \mathop{\mathrm{erf}}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1} ``` where `c_0 = 1` and ```math c_k=\sum_{m=0}^{k-1}\frac{c_m c_{k-1-m}}{(m+1)(2m+1)} = \left\{1,1,\frac{7}{6},\frac{127}{90},\frac{4369}{2520},\frac{34807}{16200},\ldots\right\} ```

## Installation ```bash npm install @stdlib/math-base-special-erfinv ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage ```javascript var erfinv = require( '@stdlib/math-base-special-erfinv' ); ``` #### erfinv( x ) Evaluates the [inverse error function][inverse-error-function]. ```javascript var y = erfinv( 0.5 ); // returns ~0.4769 y = erfinv( 0.8 ); // returns ~0.9062 y = erfinv( -1.0 ); // returns -Infinity y = erfinv( 1.0 ); // returns Infinity ``` The domain of `x` is restricted to `[-1,1]`. If `|x| > 1`, the function returns `NaN`. ```javascript var y = erfinv( -3.14 ); // returns NaN ``` If provided `NaN`, the function returns `NaN`. ```javascript var y = erfinv( NaN ); // returns NaN ``` The [inverse error function][inverse-error-function] is an [odd function][odd-function]; i.e., `erfinv(-x) = -erfinv(x)`. Thus, in accordance with the [IEEE 754][ieee754] standard, if provided `-0`, the function returns `-0`. ```javascript var y = erfinv( -0.0 ); // returns -0.0 ```

## C APIs

### Usage ```c #include "stdlib/math/base/special/erfinv.h" ``` #### stdlib_base_erfinv( x ) Evaluates the [inverse error function][inverse-error-function]. ```c double out = stdlib_base_erfinv( 0.5 ); // returns ~0.4769 out = stdlib_base_erfinv( 0.8 ); // returns ~0.9062 ``` The function accepts the following arguments: - **x**: `[in] double` input value. ```c double stdlib_base_erfinv( const double x ); ```

### Examples ```c #include "stdlib/math/base/special/erfinv.h" #include #include int main( void ) { const double x[] = { -1.0, -0.78, -0.56, -0.33, -0.11, 0.11, 0.33, 0.56, 0.78, 1.0 }; double v; int i; for ( i = 0; i < 10; i++ ) { v = stdlib_base_erfinv( x[ i ] ); printf( "x: %lf, erfinv(x): %lf\n", x[ i ], v ); } } ```

* * * ## 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 Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-erfinv.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-erfinv [test-image]: https://github.com/stdlib-js/math-base-special-erfinv/actions/workflows/test.yml/badge.svg?branch=main [test-url]: https://github.com/stdlib-js/math-base-special-erfinv/actions/workflows/test.yml?query=branch:main [coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-erfinv/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-erfinv?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-erfinv/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-special-erfinv/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-special-erfinv/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-special-erfinv/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-special-erfinv/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-special-erfinv/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-special-erfinv/blob/main/branches.md [inverse-error-function]: https://en.wikipedia.org/wiki/Error_function#Inverse_functions [maclaurin-series]: http://mathworld.wolfram.com/MaclaurinSeries.html [odd-function]: https://en.wikipedia.org/wiki/Even_and_odd_functions [ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985 [@stdlib/math/base/special/erf]: https://github.com/stdlib-js/math-base-special-erf [@stdlib/math/base/special/erfc]: https://github.com/stdlib-js/math-base-special-erfc [@stdlib/math/base/special/erfcinv]: https://github.com/stdlib-js/math-base-special-erfcinv