Computation of Spheroidal Wave Functions

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Summer research project, Middlebury College.
Advisor Dr. Noah Graham.

The abstract (written by Dr. Graham).

After his first year at Middlebury, Pavlo worked as a summer research
student developing a Mathematica software package for the computation of
spheroidal wave functions. These functions arise when one considers waves
confined within or reflecting from oblate (pancake-shaped) or prolate
(cigar-shaped) spheroidal bodies. They generalize the more common
spherical harmonics and spherical Bessel functions. Pavlo quickly mastered
both the advanced mathematics and the complex computer code involved in
this work. He rewrote sections of the code to compute Taylor expansions of
spheroidal wave functions, fixing several bugs and significantly improving
the code’s efficiency — remarkable contributions, particularly for a
first-year student. Pavlo’s careful testing and benchmarking ensured the
reliability of these changes in the wide variety of situations in which the
code could be used. This code is currently used in Dr. Graham’s
calculations of Casimir energies and forces for spheroidal geometries.

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