Generalized Laguerre polynomial
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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
Platform Compatibility
Windows macOS LinuxCategories
- MATLAB > Mathematics > Elementary Math > Polynomials >
Tags
Acknowledgements
Inspired by: AssociatedLaguerrePoly.m
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Version | Published | Release Notes | |
---|---|---|---|
1.0.0.0 | One minor pre-allocation error removed |