Asymptotic Identities for Jacobi Polynomials via Spectral Geometry of Rank-One Symmetric Spaces

Radial eigenfunctions of the Laplace-Beltrami operator on compact rank-one symmetric spaces may be expressed in terms of Jacobi polynomials. We use this fact to prove an identity for Jacobi polynomials which is inspired by results of Minakshisundaram-Pleijel and Zelditch on the Fourier coefficients of a smooth measure supported on a compact submanifold of a compact Riemannian manifold.