PsiLAB Help Manual
Page
Section:
Special Polynomials
Name:
Poly
Orthogonal Polynomials.
The Poly module provides the following polynomial functions:
- Legendre.n : Simple Legendre polynomials P (n) (x)
- Legendre.nm : Assigned Legendre polynomials P (n) (m) (x) with 0 <= m <= n
- Chebyshev.t : Chebyshev polynomial T (n) (x)
- Chebyschev.u : Chebyshev polynomial U (n) (x)
- Hermite.n : Hermite polynomaial H (n) (x)
- Laguerre.n : Simple Laguerre polynomial L (n) (x)
- Laguerre.na : Assigned Laguerre polynomial L (n) (a) (x)
All polynomials are evaluated with recurrence formulas:
P (n) (x) = [(2n-1)/n]*x*P (n-1) (x) - [(n-1)/n]* P (n-2) (x)
P (n) (m) (x) = [(2n-1)/(n-m)]*x*P (n-1) (m) (x)
- [(n+m-1)/(n-m)]*P (n-2) (m) (x)
T (n) (x) = 2*x*T (n-1) (x) - T (n-2) (x)
U (n) (x) = 2*x*U (n-1) (x) - U (n-2) (x)
H (n) (x) = 2*x*H (n-1) (x) - 2(n-1)H (n-2) (x)
L (n) (x) = [(2n-1-x)/n]*L (n-1) (x) - [(n-1)/n]*L (n-2) (x)
L (n) (m) (x)=-d/dx[L (n+1) (m-1) (x)]
Examples:
[] Poly.Laguerre.n 0.5 4 ;;
- : float = -0.330729166667
[] Poly.Legendre.nm (-0.1) 4 2 ;;
- : float = -6.90525
[] Poly.Hermite.n 10.0 3 ;;
- : float = 7880
Printed by PsiLAB