laguerre_polynomial, a Fortran77 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 information on this web page is 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.
bernstein_polynomial, a Fortran77 code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
chebyshev_polynomial, a Fortran77 code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.
gen_laguerre_rule, a Fortran90 code which can compute and print a generalized Gauss-Laguerre quadrature rule.
hermite_polynomial, a Fortran77 code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
jacobi_polynomial, a Fortran77 code which evaluates the Jacobi polynomial and associated functions.
laguerre_exactness, a Fortran77 code which tests the polynomial exactness of Gauss-Laguerre quadrature rules for integration over [0,+oo) with density function exp(-x).
laguerre_rule, a Fortran90 code which can compute and print a Gauss-Laguerre quadrature rule.
laguerre_test_int, a Fortran77 code which defines test integrands for integration over [A,+oo).
legendre_polynomial, a Fortran77 code which evaluates the Legendre polynomial and associated functions.
polpak, a Fortran77 code which evaluates a variety of mathematical functions.
polynomial_conversion, a Fortran77 code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Hermite, Lagrange, Laguerre and other forms.
test_values, a Fortran77 code which supplies test values of various mathematical functions.