Digital Library of Mathematical Functions
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29 Lamé FunctionsLamé Functions

§29.9 Stability

The Lamé equation (29.2.1) with specified values of k,h,ν is called stable if all of its solutions are bounded on ; otherwise the equation is called unstable. If ν is not an integer, then (29.2.1) is unstable iff haν0(k2) or h lies in one of the closed intervals with endpoints aνm(k2) and bνm(k2), m=1,2,. If ν is a nonnegative integer, then (29.2.1) is unstable iff haν0(k2) or h[bνm(k2),aνm(k2)] for some m=1,2,,ν.