  Measurements of Bose-Einstein correlations played a crucial role in the
discovery and the subsequent detailed exploration of the Quark-Gluon-Plasma
(QGP) created in high-energy collisions of heavy nuclei. Such measurements gave
rise to femtoscopy, a flourishing sub-field of high-energy physics, and there
are important new directions to explore and discoveries to be made in the near
future. One of these important current topics is the precise investigation of
the shape of the correlation functions utilizing L\'evy-stable sources. In this
paper, we present a novel method of calculating the shape of the two-particle
correlation functions, including the Coulomb final-state interaction. This
method relies on an exact calculation of a large part of the necessary
integrals of the Coulomb wave function and can be utilized to calculate the
correlation function for any source function with an easily accessible Fourier
transform. In this way, it is eminently applicable to L\'evy-stable source
functions. In this particular case, we find that the new method is more robust
and allows the investigation of a wider parameter range than the previously
utilized techniques. We present an easily applicable software package that is
ready to use in experimental studies.
