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ChebyshevPoly, HermitePoly, LaguerrePoly
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Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
ChebyshevPoly(N: INT, X: RINGELEM): RINGELEM
ChebyshevPoly2(N: INT, X: RINGELEM): RINGELEM
HermitePoly(N: INT, X: RINGELEM): RINGELEM
HermitePoly2(N: INT, X: RINGELEM): RINGELEM
LaguerrePoly(N: INT, X: RINGELEM): RINGELEM |
The function
ChebyshevPoly
returns the Chebyshev polynomial (of 1st
type) with index
N
, in the indeterminate
X
. The function
ChebyshevPoly2
returns the Chebyshev polynomial of 2nd type.
The function
HermitePoly
returns the
N
-th Hermite polynomial (as used
in physics); the function
HermitePoly2
returns the
N
-th Hermite
polynomial (as used in probability).
The function
LaguerrePoly
returns the
N
-th Laguerre polynomial
multiplied by
factorial(N)
(so that the coefficients are integers).
These functions also work if
X
is not an indeterminate: the result
is then the evaluation of the polynomial at the given value.
/**/ use R ::= QQ[x];
/**/ ChebyshevPoly(3,x);
4*x^3 -3*x
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