Bessel Functions in JS
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2017-07-27 14:22:02 -04:00
2017-01-05 15:04:15 -05:00
2016-10-13 13:43:49 -04:00
2016-09-24 02:15:52 -04:00

# bessel

Pure-JS implementation of Bessel functions J,Y,I,K (for the browser and nodejs). Emphasis on correctness and performance for integer order.

The standard notation is used here:

• `J` is the Bessel function of the first kind
• `Y` is the Bessel function of the second kind
• `I` is the modified Bessel function of the first kind
• `K` is the modified Bessel function of the second kind

## Installation

With npm:

``````\$ npm install bessel
``````

In the browser:

``````<script src="bessel.js"></script>
``````

The browser exposes a variable `BESSEL`

The script will manipulate `module.exports` if available (e.g. in a CommonJS `require` context). This is not always desirable. To prevent the behavior, define `DO_NOT_EXPORT_BESSEL`

## Usage

In all cases, the relevant function takes two arguments (`value`, `order`).

The return value is a JS number. `NaN` signals an error in calculation.

• `BESSEL.besselj(x, n)` computes `J_{n}(x)`

• `BESSEL.bessely(x, n)` computes `Y_{n}(x)`

• `BESSEL.besseli(x, n)` computes `I_{n}(x)`

• `BESSEL.besselk(x, n)` computes `K_{n}(x)`

For example:

``````// var BESSEL = require('bessel'); // uncomment this line if in node
BESSEL.besselj(1.5,0)              // 0.5118276712499389
BESSEL.bessely(1.5,0)              // 0.38244892476502895
BESSEL.besseli(1.5,0)              // 1.6467232021476754
BESSEL.besselk(1.5,0)              // 0.2138055693236539

var Y = BESSEL.bessely
Y(Math.PI, 5) + Y(Math.PI, 3) - (2 * 4 / Math.PI) * Y(Math.PI, 4) // 0
``````

## Testing

`make test` will run the nodejs-based test.

To generate the `excel.tsv` test cases, make a 6-column Excel Sheet:

x n `BESSELI` `BESSELJ` `BESSELK` `BESSELY`
x n `BESSELI(A1,B1)` `BESSELJ(A1,B1)` `BESSELK(A1,B1)` `BESSELY(A1,B1)`

To generate the `mma.tsv` test cases, use the Mathematica Bessel Functions:

``````(* Bessel_[value, order] *)
F[x_,n_]:={x/2,n,BesselI[n,x/2], BesselJ[n,x/2], BesselK[n,x/2], BesselY[n,x/2]}
Do[Print[ExportString[N[F[x,n],10],"csv"]], {n,1,3}, {x,1,20} ]
``````

Note: Each function follows Excel semantics `(value, order)`. Other platforms like Mathematica reverse the argument order.