calc_zeta_r
===========

.. py:function:: luminet.black_hole_math.calc_zeta_r(p: float, r: float, bh_mass: float) -> float

   Calculate :math:`\zeta_r`

   This is used for the Jacobi incomplete elliptic integral for higher-order images.

   .. math::

      \zeta_r = \arcsin \left( \sqrt{\frac{Q - P + 2M + \frac{4MP}{r}}{Q - P + 6M}} \right)

   :Parameters: * **p** (*float*) -- periastron distance
                * **r** (*float*) -- Radius in the black hole frame.
                * **bh_mass** (*float*) -- Black hole mass

   :returns: *float* -- :math:`\zeta_r`