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I'm using Gauss-Hermite quadrature to integrate

$$ \int_{-\infty}^{\infty} \! e^{-x^2} \cos x\,\mathrm{d}x $$

The exact solution is evidently $\sqrt{\pi\,\text{exp}(1/4)}$, but to be honest I don't even understand what this value is supposed to represent. How is $\cos x$ from ($-\infty,\infty$) a small, finite number? I've written code to apply the weights and abscissas for $2\text{ to } 16$ points, but the numbers I've gotten do not approach the true value and do not even converge on anything as I increase the number of points.

Would appreciate any guidance.

  • 0
    Please use TeX formatting next time.2012-04-23

3 Answers 3