{"id":19337684,"url":"https://github.com/sheetjs/bessel","last_synced_at":"2026-03-06T05:13:21.981Z","repository":{"id":7465717,"uuid":"8812745","full_name":"SheetJS/bessel","owner":"SheetJS","description":"Bessel Functions in JS","archived":false,"fork":false,"pushed_at":"2019-10-08T06:14:22.000Z","size":63,"stargazers_count":35,"open_issues_count":1,"forks_count":6,"subscribers_count":8,"default_branch":"master","last_synced_at":"2025-04-19T08:42:40.881Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"http://oss.sheetjs.com/bessel/","language":"JavaScript","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/SheetJS.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2013-03-16T02:07:44.000Z","updated_at":"2024-12-09T08:51:20.000Z","dependencies_parsed_at":"2022-09-06T11:11:47.106Z","dependency_job_id":null,"html_url":"https://github.com/SheetJS/bessel","commit_stats":null,"previous_names":[],"tags_count":4,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/SheetJS%2Fbessel","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/SheetJS%2Fbessel/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/SheetJS%2Fbessel/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/SheetJS%2Fbessel/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/SheetJS","download_url":"https://codeload.github.com/SheetJS/bessel/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":250352220,"owners_count":21416458,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-10T03:15:10.157Z","updated_at":"2026-03-06T05:13:21.607Z","avatar_url":"https://github.com/SheetJS.png","language":"JavaScript","readme":"# 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\u003cscript src=\"bessel.js\"\u003e\u003c/script\u003e\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)\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsheetjs%2Fbessel","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsheetjs%2Fbessel","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsheetjs%2Fbessel/lists"}