@stdlib/math-base-special-binet

Evaluate Binet's formula extended to real numbers.

Usage no npm install needed!

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README

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 © 2016-2022. The Stdlib Authors.