scipy tutorial - Baustatik-Info-Server

SciPy Reference Guide, Release 0.8.dev
jacobi(n, alpha, beta, monic=0)
Returns the nth order Jacobi polynomial, P^(alpha,beta)_n(x) orthogonal over [-1,1] with weighting function
(1-x)**alpha (1+x)**beta with alpha,beta > -1.
laguerre(n, monic=0)
Return the nth order Laguerre polynoimal, L_n(x), orthogonal over [0,inf) with weighting function exp(-x)
genlaguerre(n, alpha, monic=0)
Returns the nth order generalized (associated) Laguerre polynomial, L^(alpha)_n(x), orthogonal over [0,inf)
with weighting function exp(-x) x**alpha with alpha > -1
hermite(n, monic=0)
Return the nth order Hermite polynomial, H_n(x), orthogonal over (-inf,inf) with weighting function exp(-x**2)
hermitenorm(n, monic=0)
Return the nth order normalized Hermite polynomial, He_n(x), orthogonal over (-inf,inf) with weighting function
exp(-(x/2)**2)
gegenbauer(n, alpha, monic=0)
Return the nth order Gegenbauer (ultraspherical) polynomial, C^(alpha)_n(x), orthogonal over [-1,1] with
weighting function (1-x**2)**(alpha-1/2) with alpha > -1/2
sh_legendre(n, monic=0)
Returns the nth order shifted Legendre polynomial, P^*_n(x), orthogonal over [0,1] with weighting function 1.
sh_chebyt(n, monic=0)
Return nth order shifted Chebyshev polynomial of first kind, Tn(x). Orthogonal over [0,1] with weight function
(x-x**2)**(-1/2).
sh_chebyu(n, monic=0)
Return nth order shifted Chebyshev polynomial of second kind, Un(x). Orthogonal over [0,1] with weight
function (x-x**2)**(1/2).
sh_jacobi(n, p, q, monic=0)
Returns the nth order Jacobi polynomial, G_n(p,q,x) orthogonal over [0,1] with weighting function (1-x)**(p-q)
(x)**(q-1) with p>q-1 and q > 0.
Warning: Large-order polynomials obtained from these functions are numerically unstable.
orthopoly1d objects are converted to poly1d, when doing arithmetic. numpy.poly1d works in power
basis and cannot represent high-order polynomials accurately, which can cause significant inaccuracy.
Hypergeometric Functions
hyp2f1(x1,
x2, x3)
y=hyp2f1(a,b,c,z) returns the gauss hypergeometric function
hyp1f1(x1,
x2)
y=hyp1f1(a,b,x) returns the confluent hypergeometeric function
hyperu(x1,
x2)
y=hyperu(a,b,x) returns the confluent hypergeometric function of the
hyp0f1(v, z) Confluent hypergeometric limit function 0F1.
hyp2f0(x1, (y,err)=hyp2f0(a,b,x,type) returns (y,err) with the hypergeometric function 2F0 in y and an error
x2, x3, out1) estimate in err. The input type determines a convergence factor and
hyp1f2(x1, (y,err)=hyp1f2(a,b,c,x) returns (y,err) with the hypergeometric function 1F2 in y and an error
x2, x3, out1) estimate in err.
hyp3f0(x1, (y,err)=hyp3f0(a,b,c,x) returns (y,err) with the hypergeometric function 3F0 in y and an error
x2, x3, out1) estimate in err.
438 Chapter 3. Reference