# laguerre_polynomial

laguerre_polynomial, a MATLAB code which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.

The Laguerre polynomial L(n,x) can be defined by:

```        L(n,x) = exp(x)/n! * d^n/dx^n ( exp(-x) * x^n )
```
where n is a nonnegative integer.

The generalized Laguerre polynomial Lm(n,m,x) can be defined by:

```        Lm(n,m,x) = exp(x)/(x^m*n!) * d^n/dx^n ( exp(-x) * x^(m+n) )
```
where n and m are nonnegative integers.

The Laguerre function can be defined by:

```        Lf(n,alpha,x) = exp(x)/(x^alpha*n!) * d^n/dx^n ( exp(-x) * x^(alpha+n) )
```
where n is a nonnegative integer and -1.0 < alpha is a real number.

### Languages:

laguerre_polynomial is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

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### Reference:

1. Theodore Chihara,
An Introduction to Orthogonal Polynomials,
Gordon and Breach, 1978,
ISBN: 0677041500,
LC: QA404.5 C44.
2. Walter Gautschi,
Orthogonal Polynomials: Computation and Approximation,
Oxford, 2004,
ISBN: 0-19-850672-4,
LC: QA404.5 G3555.
3. Frank Olver, Daniel Lozier, Ronald Boisvert, Charles Clark,
NIST Handbook of Mathematical Functions,
Cambridge University Press, 2010,
ISBN: 978-0521192255,
LC: QA331.N57.
4. Gabor Szego,
Orthogonal Polynomials,
American Mathematical Society, 1992,
ISBN: 0821810235,
LC: QA3.A5.v23.

### Source Code:

Last revised on 12 January 2021.