# Generalized Laguerre polynomial (Scripts) 1.0

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• Last update: 5 years ago
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Mattthias Trampisch
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## Generalized Laguerre polynomial (Scripts) Publisher's description

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

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 SzegГ¶: Orthogonal Polynomials, 1958, formula (5.1.10)

#### System Requirements:

MATLAB 7.3 (R2006b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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