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Plack law of radiation

$$

B(\nu) = \frac{2\,h\,\nu^3}{c^2(e^{h\nu/kT}-1)}

$$

I want to show that for small frequencies, Reyleigh-Jeans law:

$$

B(\nu) = \frac{2\nu^2kT}{c^2}

$$

is correct.

I take the limit of Planck law as ##\nu \to 0## using l'hopital rule:

$$

\lim_{\nu \to 0} \frac{2\,h}{c^2} \frac{\nu^3}{e^{h\nu/kT}-1} \stackrel{\text{l'H}}{=} \lim_{\nu \to 0} \frac{2\,h}{c^2} \frac{3\nu^2kT}{e^{h\nu/kT}h} = 0

$$

I am off by a factor of 3. What is wrong with my maths?

Thank you for your time.

Kind regards,

Marius

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# Deriving the rayleigh-jeans limit of planck law of radiation

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