  Completeness relations are associated through Mercer's theorem to complete
orthonormal basis of square integrable functions, and prescribe how a Dirac
delta function can be decomposed into basis of eigenfunctions of a
Sturm-Liouville problem. We use Gegenbauer's addition theorem to prove a
relation very close to a completeness relation, but for a set of Bessel
functions not known to form a complete basis in $L^2[0, 1]$.
