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Planck's Radiation Function


The function

f(x)={1\over x^5(e^{1/x}-1)}.

It has a Maximum at $x\approx 0.201405$, where

f'(x)={5x-e^{1/x}(5x-1)\over x^7(e^{1/x}-1)^2}=0,

and inflection points at $x\approx 0.11842$ and $x\approx 0.283757$, where

f''(x)={e^{1/x}(1+e^{1/x})+6x(e^{1/x}-1)[e^{1/x}(5x-2)-5x]\over (e^{1/x}-1)^3 x^9}=0.
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Abramowitz, M. and Stegun, C. A. (Eds.). ``Planck's Radiation Function.'' §27.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 999, 1972.

© 1996-9 Eric W. Weisstein