Abstract In this short note, we build upon recent results from our earlier paper to present a precise expression for the asymptotic variance of the Euler-Poincaré characteristic for the excursion sets ...

THE need for a treatise on harmonic analysis, more particularly on spherical harmonics, has been recognised for a long time by mathematicians who teach the subject or who find it necessary to use ...

THIS treatise contains, in an expanded form, the subject-matter of a course of lectures by Prof. Byerly, on the functions mentioned in the title. The properties of the functions are developed, to a ...