  Lame equation arises from deriving Laplace equation in ellipsoidal
coordinates; in other words, it's called ellipsoidal harmonic equation. Lame
function is applicable to diverse areas such as boundary value problems in
ellipsoidal geometry, chaotic Hamiltonian systems, the theory of Bose-Einstein
condensates, etc.
  By applying generating function into modern physics (quantum mechanics,
thermodynamics, black hole, supersymmetry, special functions, etc), we are able
to obtain the recursion relation, a normalization constant for the wave
function and expectation values of any physical quantities. For the case of
hydrogen-like atoms, generating function of associated Laguerre polynomial has
been used in order to derive expectation values of position and momentum. By
applying integral forms of Lame polynomial in the Weierstrass's form in which
makes B_n term terminated [29], I consider generating function of it including
all higher terms of A_n's.
  This paper is 8th out of 10 in series "Special functions and three term
recurrence formula (3TRF)". See section 4 for all the papers in the series.
Previous paper in series deals with the power series expansion and the integral
formalism of Lame equation in the Weierstrass's form and its asymptotic
behavior [29]. The next paper in the series describes analytic solution for
grand confluent hypergeometric function [31].
