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How do we numerically integrate a rapidly decaying exponential function? A simple Gauss quadrature which is based on approximating the function by polynomial, I think will not work, since rapidly decaying exponential function will require more terms in the series. Is there a series approximation for the function?

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    I'm able integrate using simpson's rule. But the number of function evaluation is more.2010-12-24

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Variable substitution to make $k=1$, and use Gauss-Laguerre. For more advanced method, the double exponential transformation maybe relevant.

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    I'll give a try and get back to you, if you don't mind.. thanks!2010-12-24