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

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

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

Examples

See :

Local connectivity graph

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Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /scipy/special/_orthogonal.py#167
type: <class 'function'>
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