maths
=====

Panoply of Math Functions for NodeJS.

To build this, npm install -g voc and voc README.md

Code

``json>package.json
{
"version": "0.1.0",
"dependencies": {
`

Gamma Function

substack's gamma library provides the regular
gamma function:

`json>package.json
"gamma":"",
`

The gamma function takes a single real parameter.

`js>maths.js
var gamma = require('gamma');
exports.gamma = gamma;
`

Both matlab and Excel use the function name gammaln to refer to the natural
log of the gamma function. Mathematica uses the name LogGamma and scipy uses
the name loggamma. Both names will be used:

`
exports.gammaln = gamma.log;
exports.loggamma = gamma.log;
`

Gamma's Friends

The regular beta function is a straightforward manipulation of gamma:

`js>maths.js
var beta = function(a,b) { return (gamma(a)*gamma(b))/gamma(a+b); };
var betaln = function(a,b) { return gamma.log(a)+gamma.log(b)-gamma.log(a+b); };
beta.log = betaln;
exports.beta = beta;
exports.betaln = betaln;
`

The lesser-known Pochhammer symbol is even simpler (uses Mathematica order):

`
var pochhammer = function(a,n) { return gamma(a+n) / gamma(a); };
var pochhammerln = function(a,n) { return gamma.log(a+n) - gamma.log(a); };
pochhammer.log = pochhammerln;
exports.pochhammer = pochhammer;
exports.pochhammerln = pochhammerln;
`

Bessel Functions

SheetJS's bessel library provides the Bessel
functions:

`json>package.json
"bessel":"",
`

The bessel functions accept the parameters (x, n) where n is the order of
the solution and x is the point at which to evaluate:

`js>maths.js
var bessel = require('bessel');
exports.besselj = bessel.besselj;
exports.bessely = bessel.bessely;
exports.besseli = bessel.besseli;
exports.besselk = bessel.besselk;
`

Fractions

SheetJS's frac library provides the frac function for
rational approximations to numbers:

`json>package.json
"frac":"",
`

The frac function accept the parameters (x, D, m) where x is the number you
wish to approximate, D is an upper bound on the denominator, and m is a flag
indicating that you want mixed rather than improper fractions:

`js>maths.js
var frac = require('frac');
exports.frac = frac;
`

Miscellaneous

`json>package.json
"voc":""
},
"name": "maths",
"author": "SheetJS",
"description": "Panoply of Math Functions for NodeJS",
"keywords": ["math", "maths", "specfun", "scimath"],
"repository":{ "type": "git", "url": "https://github.com/SheetJS/maths.git" },
"main": "maths.js"
}
``