mrpy.base.core.entire_integral¶
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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