scipy tutorial - Baustatik-Info-Server

eval_hermite()
Evaluate Hermite polynomial at a point.
eval_hermitenorm()
Evaluate normalized Hermite polynomial at a point.
eval_gegenbauer()
Evaluate Gegenbauer polynomial at a point.
eval_sh_legendre()
Evaluate shifted Legendre polynomial at a point.
eval_sh_chebyt()
Evaluate shifted Chebyshev T polynomial at a point.
eval_sh_chebyu()
Evaluate shifted Chebyshev U polynomial at a point.
eval_sh_jacobi()
Evaluate shifted Jacobi polynomial at a point.
SciPy Reference Guide, Release 0.8.dev
The functions below, in turn, return orthopoly1d objects, which functions similarly as numpy.poly1d. The orthopoly1d
class also has an attribute weights which returns the roots, weights, and total weights for the appropriate form of
Gaussian quadrature. These are returned in an n x 3 array with roots in the first column, weights in the second
column, and total weights in the final column.
legendre(n[, monic]) Returns the nth order Legendre polynomial, P_n(x), orthogonal over
chebyt(n[, monic]) Return nth order Chebyshev polynomial of first kind, Tn(x). Orthogonal
chebyu(n[, monic]) Return nth order Chebyshev polynomial of second kind, Un(x). Orthogonal
chebyc(n[, monic]) Return nth order Chebyshev polynomial of first kind, Cn(x). Orthogonal
chebys(n[, monic]) Return nth order Chebyshev polynomial of second kind, Sn(x). Orthogonal
jacobi(n, alpha, beta[, monic]) Returns the nth order Jacobi polynomial, P^(alpha,beta)_n(x)
laguerre(n[, monic]) Return the nth order Laguerre polynoimal, L_n(x), orthogonal over
genlaguerre(n, alpha[, monic]) Returns the nth order generalized (associated) Laguerre polynomial,
hermite(n[, monic]) Return the nth order Hermite polynomial, H_n(x), orthogonal over
hermitenorm(n[, monic]) Return the nth order normalized Hermite polynomial, He_n(x), orthogonal
gegenbauer(n, alpha[, monic]) Return the nth order Gegenbauer (ultraspherical) polynomial,
sh_legendre(n[, monic]) Returns the nth order shifted Legendre polynomial, P^*_n(x), orthogonal
sh_chebyt(n[, monic]) Return nth order shifted Chebyshev polynomial of first kind, Tn(x).
sh_chebyu(n[, monic]) Return nth order shifted Chebyshev polynomial of second kind, Un(x).
sh_jacobi(n, p, q[, monic]) Returns the nth order Jacobi polynomial, G_n(p,q,x)
legendre(n, monic=0)
Returns the nth order Legendre polynomial, P_n(x), orthogonal over [-1,1] with weight function 1.
chebyt(n, monic=0)
Return nth order Chebyshev polynomial of first kind, Tn(x). Orthogonal over [-1,1] with weight function
(1-x**2)**(-1/2).
chebyu(n, monic=0)
Return nth order Chebyshev polynomial of second kind, Un(x). Orthogonal over [-1,1] with weight function
(1-x**2)**(1/2).
chebyc(n, monic=0)
Return nth order Chebyshev polynomial of first kind, Cn(x). Orthogonal over [-2,2] with weight function
(1-(x/2)**2)**(-1/2).
chebys(n, monic=0)
Return nth order Chebyshev polynomial of second kind, Sn(x). Orthogonal over [-2,2] with weight function
(1-(x/)**2)**(1/2).
3.17. Special functions (scipy.special) 437