@stdlib/math-base-special-binet
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    0.0.5 • Public • Published

    Binet's Formula

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    Evaluate Binet's formula extended to real numbers.

    Binet's formula refers to the closed-form solution for computing the nth Fibonacci number and may be expressed

    Binet's formula

    where φ is the golden ratio and ψ is 1 - φ. To extend Fibonacci numbers to real numbers, we may express Binet's formula as

    Binet's formula extended to real numbers.

    Installation

    npm install @stdlib/math-base-special-binet

    Usage

    var binet = require( '@stdlib/math-base-special-binet' );

    binet( x )

    Evaluates Binet's formula extended to real numbers.

    var v = binet( 0.0 );
    // returns 0.0
    
    v = binet( 1.0 );
    // returns 1.0
    
    v = binet( 2.0 );
    // returns 1.0
    
    v = binet( 3.0 );
    // returns 2.0
    
    v = binet( -1.0 );
    // returns 1.0
    
    v = binet( 3.14 );
    // returns ~2.12

    If provided NaN, the function returns NaN.

    var v = binet( NaN );
    // returns NaN

    Notes

    • The function returns only approximate Fibonacci numbers for nonnegative integers.
    • The function does not return complex numbers, guaranteeing real-valued return values.

    Examples

    var binet = require( '@stdlib/math-base-special-binet' );
    
    var v;
    var i;
    
    for ( i = 0; i < 79; i++ ) {
        v = binet( i );
        console.log( v );
    }

    Notice

    This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

    For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-special-binet

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    9

    Version

    0.0.5

    License

    Apache-2.0

    Unpacked Size

    52.3 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser