gaussQuadComplex

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gaussQuadComplex#

Given a straight line segment \(\gamma\subset\mathbb{C}\) with endpoints \(a\) and \(b\), this subtroutine produces a Gauss Legendre quadrature rule

\[ \sum_{j=1}^N w_j f(z_j) \approx \int_\gamma f(z) \mathrm{d}z . \]
[z,w,dz] = gaussQuadComplex(a,b,numPts)

Inputs#

  • a and b : The endpoints of the straight line segment \(\gamma\).

  • numPts : The number of quadrature points, \(N\) in the above approximation.

Outputs#

  • z : The quadrature points \(z_j\).

  • w : The quadrature weights \(w_j\).

  • dz : An array of identical unit length complex numbers corresponding to the complex argument of \(b-a\).

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