roots_chebyc — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.roots_chebyc(n, mu=False)[source]#

Gauss-Chebyshev (first kind) quadrature.

Compute the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree Chebyshev polynomial of the first kind, \(C_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-2, 2]\)with weight function \(w(x) = 1 / \sqrt{1 - (x/2)^2}\). See 22.2.6 in [AS] for more details.

Parameters:

nint

quadrature order

mubool, optional

If True, return the sum of the weights, optional.

Returns:

xndarray

Sample points

wndarray

Weights

mufloat

Sum of the weights

References

[AS]

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.