ON THE ROLE OF THE "LEMNISCATIC CORE" IN LAME ELLIPSOIDAL COORDI-NATES

Abstract The functions introduced by Gabriel Lamé in connection with the distribution of heat in a homogeneous ellipsoid [1-2], which have since been given Lamé's name, have become the subject of a large number of studies. The works of Liouville and Heine [3-4], independent but simultaneous, are the first in history and among the most important. Then come the excellent studies of Charles Hermite, continued by various authors on the integration of the differential equation satisfied by these functions. Closer to them are two separate groups of significant works: F. Klein [5-6] and his students generalize the Lamé functions and consider them in a completely new way.