Examples
User documentation
Here are some functions for constructing individual members of certain families of orthogonal polynomials.
Constructors and pseudo-constructors
Let n
be a non-negative integer, and x
a ring element
(typically an indeterminate or a number). The functions below
evaluate the corresponding polynomial at x
: if x
is an
indeterminate then the polynomial itself is returned.
ChebyshevPoly(n,x)
Chebyshev polynomial of 1st kindChebyshevPoly2(n,x)
Chebyshev polynomial of 2nd kindHermitePoly(n,x)
Hermite polynomial (physics)HermitePoly2(n,x)
Hermite polynomial (probability)LaguerrePoly(n,x)
Laguerre polynomomial multiplied byfactorial(n)
DicksonPoly(x,n,alpha)
Dickson polynomial of 1st type not orthogDicksonPoly2(x,n,alpha)
Dickson polynomial of 2nd type not orthog
Maintainer documentation
Some of the Chebyshev functions are not used, but I left them there in case they ever become useful.
Bugs, shortcomings and other ideas
The dispatch functions for Hermite polynomials have not been tested; so I do not know if the criterion for choosing between "explicit" and "iterative" implementations actually makes any sense.
Main changes
2017
- October (v0.99560): first release 2018
- November (v0.99610): added DicksonPoly