def entire_integral(logHs, alpha, beta, s=1):
r"""
The entire integral of the un-normalised mass-weighted *non-truncated* MRP:
.. math:: \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, :math:`H_\star`.
alpha : array_like
The power-law index
beta : array_like
Exponential cutoff parameter
s : array_like, optional
Weighting (or `scaling`) of the integral.
"""
return 10**((s + 1)*logHs)*sp.gamma((alpha + 1 + s)/beta)
def _gammaz(self):
"""
The gamma function at z=(1+a)/b. Stored for use elsewhere.
"""
return sp.gamma(self._z)
def _gammazd(self):
return sp.gamma(self._zd)
