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bessel\n\nPure-JS implementation of Bessel functions J,Y,I,K (for the browser and nodejs).\nEmphasis on correctness and performance for integer order.\n\nThe standard notation is used here:\n\n - `J` is the Bessel function of the first kind\n - `Y` is the Bessel function of the second kind\n - `I` is the modified Bessel function of the first kind\n - `K` is the modified Bessel function of the second kind\n\n## Installation\n\nWith [npm](https://www.npmjs.org/package/bessel):\n\n```bash\n$ npm install bessel\n```\n\nIn the browser:\n\n```html\n<script src=\"bessel.js\"></script>\n```\n\nThe browser exposes a variable `BESSEL`\n\nThe script will manipulate `module.exports` if available (e.g. in a CommonJS\n`require` context).  This is not always desirable.  To prevent the behavior,\ndefine `DO_NOT_EXPORT_BESSEL`\n\n## Usage\n\nIn all cases, the relevant function takes two arguments (`value`, `order`).\n\nThe return value is a JS number.  `NaN` signals an error in calculation.\n\n- `BESSEL.besselj(x, n)` computes `J_{n}(x)`\n\n- `BESSEL.bessely(x, n)` computes `Y_{n}(x)`\n\n- `BESSEL.besseli(x, n)` computes `I_{n}(x)`\n\n- `BESSEL.besselk(x, n)` computes `K_{n}(x)`\n\nFor example:\n\n```js\n// var BESSEL = require('bessel'); // uncomment this line if in node\nBESSEL.besselj(1.5,0)              // 0.5118276712499389\nBESSEL.bessely(1.5,0)              // 0.38244892476502895\nBESSEL.besseli(1.5,0)              // 1.6467232021476754\nBESSEL.besselk(1.5,0)              // 0.2138055693236539\n\nvar Y = BESSEL.bessely\nY(Math.PI, 5) + Y(Math.PI, 3) - (2 * 4 / Math.PI) * Y(Math.PI, 4) // 0\n```\n\n## Testing\n\n`make test` will run the nodejs-based test.\n\nTo generate the `excel.tsv` test cases, make a 6-column Excel Sheet:\n\n| x | n |    `BESSELI`   |    `BESSELJ`   |    `BESSELK`   |    `BESSELY`   |\n|---|---|:--------------:|:--------------:|:--------------:|:--------------:|\n| x | n |`BESSELI(A1,B1)`|`BESSELJ(A1,B1)`|`BESSELK(A1,B1)`|`BESSELY(A1,B1)`|\n\nTo generate the `mma.tsv` test cases, use the Mathematica Bessel Functions:\n\n```mathematica\n(* Bessel_[value, order] *)\nF[x_,n_]:={x/2,n,BesselI[n,x/2], BesselJ[n,x/2], BesselK[n,x/2], BesselY[n,x/2]}\nDo[Print[ExportString[N[F[x,n],10],\"csv\"]], {n,1,3}, {x,1,20} ]\n```\n\nNote: Each function follows Excel semantics `(value, order)`.  Other platforms\nlike Mathematica reverse the argument order.\n\n## License\n\nPlease consult the attached LICENSE file for details.  All rights not explicitly\ngranted by the Apache 2.0 License are reserved by the Original Author.\n\n## Badges\n\n[![Build Status](https://saucelabs.com/browser-matrix/bessel.svg)](https://saucelabs.com/u/bessel)\n\n[![Build Status](https://travis-ci.org/SheetJS/bessel.svg?branch=master)](https://travis-ci.org/SheetJS/bessel)\n\n[![Coverage Status](http://img.shields.io/coveralls/SheetJS/bessel/master.svg)](https://coveralls.io/r/SheetJS/bessel?branch=master)\n\n[![NPM Downloads](https://img.shields.io/npm/dt/bessel.svg)](https://npmjs.org/package/bessel)\n\n[![Dependencies Status](https://david-dm.org/sheetjs/bessel/status.svg)](https://david-dm.org/sheetjs/bessel)\n\n[![ghit.me](https://ghit.me/badge.svg?repo=sheetjs/bessel)](https://ghit.me/repo/sheetjs/bessel)\n\n[![Analytics](https://ga-beacon.appspot.com/UA-36810333-1/SheetJS/bessel?pixel)](https://github.com/SheetJS/bessel)","users":{}}