erf / erfc

Inverse error function and inverse complementary error function.

Evaluates the inverse error and inverse complementary error functions.

This package is a rewrite of math-erfinv and math-erfcinv in Typescript. This package supports both CommonJs and ES Modules.

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The inverse error function is defined as

$$\mathrm{erf}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}$$

where c_0 = 1 and

$$c_k=\sum_{m=0}^{k-1}\frac{c_m c_{k-1-m}}{(m+1)(2m+1)} = \left\{1,1,\frac{7}{6},\frac{127}{90},\frac{4369}{2520},\frac{34807}{16200},\ldots\right\}$$

The inverse complementary error function is defined as

$$\mathrm{erfc}^{-1}(1-z) = \mathrm{erf}^{-1}(z)$$

Installation

$ npm install @toshiara/special-erfinv

Usage

// for CommonJs
const { erfinv, erfcinv } = require('@toshiara/special-erfinv');

// for ES Modules
import { erfinv, erfcinv } from '@toshiara/special-erfinv';

erf(x)

Evaluates the inverse error function.

erfinv(0.1);
// returns 0.08885599049425769

erfinv(0.4);
// returns 0.37080715859355795

erfinv(0.85);
// returns 1.0179024648320276

erfinv(-1);
// returns -Infinity

erfinv(1);
// returns Infinity

If provided NaN, the function returns NaN.

erfinv(NaN);
// returns NaN

erfinvc(x)

Evaluates the inverse complementary error function.

erfcinv(0.2);
// returns 0.9061938024368231

erfcinv(0.4);
// returns 0.5951160814499948

erfcinv(0.85);
// returns 0.13372692166481973

erfcinv(0);
// returns Infinity

erfcinv(2);
// returns -Infinity

If provided NaN, the function returns NaN.

erfcinv(NaN);
// returns NaN

License

MIT license.

Copyright

Copyright © 2016. The Compute.io Authors.