F = 2 h c2 -5 / (exp(hc/kT) - 1).
or, combining the constants:
F = c1 -5 / exp(c2 /T) - 1),
where c1 = 2 hc2 = 3.7419 × 10-5 erg cm2 s-1 [ in cm]
and c2 = hc/k = 1.4288 cm °K.
On the red side of the distribution (when T >> 1) the denominator approaches zero as x => 0 and ex => 1. For small values of the exponent, the series expansion for the exponential can be used as an excellent approximation of the value of the exponential.
ex = 1 + x + x2/2! + x3/3! + x4/4! + . . .
But when x is very small, all terms beyond the first in x can be ignored, allowing us to use:
ex = 1 + x
Making this substitution, we obtain:
F = c1 -5 / (1 + c2 /T - 1),
F = (c1/c2) T -4.
This expression for the blackbody distribution on the red side of the maximum of the Planck curve is called the Rayleigh-Jeans Distribution.