Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 15, pp. 1-30.

Title: The Heun equation and the Calogero-Moser-Sutherland system II:
       Perturbation and algebraic solution

Author: Kouichi Takemura (Yokohama City University, Japan)

Abstract: 
 We apply a method of perturbation for the $BC_1$ Inozemtsev model 
 from the trigonometric model and show the holomorphy of perturbation.
 Consequently, the convergence of eigenvalues and eigenfuncions which 
 are expressed as formal power series is proved.
 We investigate also the relationship between $L^2$ space and some 
 finite dimensional space of elliptic functions.

Submitted May 15, 2003. Published February 5, 2004.
Math Subject Classifications: 33E15, 81Q10.
Key Words: Heun equation; Calogero-Moser-Sutherland system; 
      Inozemtsev model; perturbation; Kato-Rellich theory; 
      trigonometric limit; Heun function; algebraic solution.