Generalized Laguerre polynomial

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha} for real valued alphas
4.8K Downloads
Updated 16 Aug 2007

No License

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha}

This function computes the generalized Laguerre polynomial L{n,alpha}.
If no alpha is supplied, alpha is set to zero and this function calculates the "normal" Laguerre polynomial.

Input:
- n = nonnegative integer as degree level
- alpha >= -1 real number (input is optional)

The output is formated as a polynomial vector of degree (n+1) corresponding to MATLAB norms (that is the highest coefficient is the first element).

Possible usage:
- polyval(LaguerreGen(n, alpha), x) evaluates L{n, alpha}(x)
- roots(LaguerreGen(n, alpha)) calculates roots of L{n, alpha}

Calculation is done recursively using matrix operations for very fast execution time. The formula is taken from Szegö: Orthogonal Polynomials, 1958, formula (5.1.10)

Cite As

Mattthias Trampisch (2024). Generalized Laguerre polynomial (https://www.mathworks.com/matlabcentral/fileexchange/15916-generalized-laguerre-polynomial), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2006b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Polynomials in Help Center and MATLAB Answers
Acknowledgements

Inspired by: AssociatedLaguerrePoly.m

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.0.0.0

One minor pre-allocation error removed