= Blackbody ionizing photon function
{title2=$F(y)=\int_y^\infty x^2/(e^x-1)\,dx$}
A spherical <blackbody> star emits $Q(E_0)=8\pi^2R_s^2(kT_s)^3F(E_0/kT_s)/(h^3c^2)$ photons per time above threshold $E_0$. Integrating <specific intensity> over the outward hemisphere gives flux $\pi B_\nu$; dividing the resulting <spectral luminosity> by photon energy and substituting $x=h\nu/kT_s$ proves the formula. The convergent series $F(y)=\sum_{m\geq1}e^{-my}(y^2/m+2y/m^2+2/m^3)$ follows by integrating the geometric-series expansion termwise.
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