Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

Understand

The spheroidal harmonics $S_{lm}(\theta;c)$ have attracted the attention of both physicists and mathematicians over the years.

• These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects.
• The asymptotic eigenvalues $\{A_{lm}(c)\}$ of these functions have been determined by many authors.
• However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\to\infty$ with a fixed value of $c$, or to the complementary regime $|c|\to\infty$ with a fixed value of $m$.