Abstract
We consider the generalized Lamé equation with A = α + βk−21, B = γk−22 + δk−21 + λ. By introducing a generalization of Jacobi's elliptic functions, we transform this equation to a Schrödinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the parameters (α, β, γ, δ, λ) quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.
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