mrpy.base.core.entire_integral

mrpy.base.core.entire_integral(logHs, alpha, beta)

The entire integral of the un-normalised mass-weighted non-truncated MRP:

\[\int_0^\infty m^s f(m) = \mathcal{H}_\star^{s+1} \Gamma\left(\frac{\alpha+1+s}{\beta}\right) \ dm.\]

where s defines a weighting of the integral, in which the immediate application is that s=1 gives the total mass density.

Note

The sum of alpha and s must be greater than -1.

Parameters:

logHs : array_like

The base-10 logarithm of the scale mass, \(H_\star\).

alpha : array_like

The power-law index

beta : array_like

Exponential cutoff parameter