suivant: Tchebychev polynomials of first
monter: Orthogonal polynomials
précédent: Hermite polynomial : hermite
Table des matières
Index
Laguerre polynomials: laguerre
laguerre takes as argument an integer n and optionnally
a variable name (by default x) and a parameter name (by default a).
laguerre returns the Laguerre polynomial of degree n and of
parameter a.
If L(n, a, x) denotes the Laguerre polynomial of degree n and
parameter a, the following recurrence relation holds:
L(0,
a,
x) = 1,
L(1,
a,
x) = 1 +
a -
x,
L(
n,
a,
x) =
L(
n - 1,
a,
x) -
L(
n - 2,
a,
x)
These polynomials are orthogonal for the scalar product
<
f,
g > =
f (
x)
g(
x)
xae-xdx
Input :
laguerre(2)
Output :
(a^
2+-2*a*x+3*a+x^
2+-4*x+2)/2
Input :
laguerre(2,y)
Output :
(a^
2+-2*a*y+3*a+y^
2+-4*y+2)/2
Input :
laguerre(2,y,b)
Output :
(b^
2+-2*b*y+3*b+y^
2+-4*y+2)/2
giac documentation written by Renée De Graeve and Bernard Parisse