= Einstein-de Sitter spectral-background convergence criterion
{c}
{title2=$\alpha<3/2$}
For nonevolving <comoving number density> $n_0$, identical spectra $L_\nu\propto\nu^\alpha$, and no attenuation, the <cosmological background intensity from comoving emissivity> in an <Einstein-de Sitter universe> is proportional to $\int_0^\infty(1+z)^{\alpha-5/2}dz$. The <improper integral> is finite exactly for $\alpha<3/2$, with value $1/(3/2-\alpha)$. Equality gives logarithmic divergence; larger $\alpha$ gives a power-law divergence. A formation epoch or a spectral break can regularize this idealized model.
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