`scipy.special._orthogonal:_gen_roots_and_weights`

source: /scipy/special/_orthogonal.py :159

Signature

   def     _gen_roots_and_weights (    n    ,    mu0    ,    an_func    ,    bn_func    ,    f    ,    df    ,    symmetrize    ,    mu      )

Summary

[x,w] = gen_roots_and_weights(n,an_func,sqrt_bn_func,mu)

Extended Summary

Returns the roots (x) of an nth order orthogonal polynomial, and weights (w) to use in appropriate Gaussian quadrature with that orthogonal polynomial.

The polynomials have the recurrence relation: P_n+1(x) = (x - A_n) P_n(x) - B_n P_n-1(x)

an_func(n) should return A_n sqrt_bn_func(n) should return sqrt(B_n) mu ( = h_0 ) is the integral of the weight over the orthogonal interval

Aliases

scipy.special._orthogonal._gen_roots_and_weights