laguerre_polynomial, a Python 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.
The computer code and data files described and made available on this web page are distributed under the MIT license.
laguerre_polynomial is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
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