:mod:`lamberthub.utils.stumpff`
===============================

.. py:module:: lamberthub.utils.stumpff
   :noindex:

.. autoapi-nested-parse::

   This module holds the so-called Stumpff functions. These set of functions
   usually appear in a plethora of equations within the subject of astrodynamics.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::


   lamberthub.utils.stumpff.c2


   lamberthub.utils.stumpff.c3



.. py:function:: c2(psi)

   Second Stumpff function.

   For positive arguments:

   .. math::

       c_2(\psi) = \frac{1 - \cos{\sqrt{\psi}}}{\psi}



.. py:function:: c3(psi)

   Third Stumpff function.

   For positive arguments:

   .. math::

       c_3(\psi) = \frac{\sqrt{\psi} - \sin{\sqrt{\psi}}}{\sqrt{\psi^3}}