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Evaluating Plank's Law

Roy Vincent L. Canseco, MSEE        Jan 2014

Plank’s law for Black-Body radiation takes the form

Plotting the integrand

The plot suggests that approximating the integral from 0 to infinity can be done by numerically integrating from 0 to 15.

We use the Maple implementation of the Quadrature rule with the following parameters: composite, non-adaptive and Simpson-based. We integrate from 0 to 15 and again from 0 to 20  in order to compare if there is any significant improvement from the truncating the integration at a further interval. The above plot suggests that there shouldn’t be any significant change in value.


There is less than 1% change in value, suggesting a good enough balance between efficiency and accuracy.