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Add Gauss-chebyshev to integration.md

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Andrew Cumming 2023-09-17 17:28:17 -04:00
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integration.md
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@ -145,7 +145,11 @@ Modify your code to use the Gauss-Hermite coefficients and check that you can ge
Hint: If you want to use `scipy.integrate.quad` again to get the value of the integral as a comparison, note that you can give it limits of $-\infty$ to $+\infty$ using `-np.inf` and `np.inf`. Hint: If you want to use `scipy.integrate.quad` again to get the value of the integral as a comparison, note that you can give it limits of $-\infty$ to $+\infty$ using `-np.inf` and `np.inf`.
``` ```
Another example is $W(x)=e^{-x}$ with integration limits $0$ to $\infty$. In this case, we need Gauss-Laguerre integration -- see [`numpy.polynomial.laguerre.laggauss`](https://numpy.org/doc/stable/reference/generated/numpy.polynomial.laguerre.laggauss.html). Other examples are
- $W(x)=e^{-x}$ with integration limits $0$ to $\infty$. In this case, we need Gauss-Laguerre integration -- see [`numpy.polynomial.laguerre.laggauss`](https://numpy.org/doc/stable/reference/generated/numpy.polynomial.laguerre.laggauss.html)
- $W(x)=1/\sqrt{1-x^2}$ from $x=-1$ to $1$ is Gauss-Chebyshev quadrature -- see
[`numpy.polynomial.chebyshev.chebgauss`](https://numpy.org/doc/stable/reference/generated/numpy.polynomial.chebyshev.chebgauss.html)
## Integration challenge ## Integration challenge