On Lame's equation of a particular kind

Details On Lame's equation of a particular kind On Lame's equation of a particular kind

2000-08-03

arxiv.org/abs/math-ph/0008008v2

J. Phys. A: Math. Gen. 34 No 39 (5 October 2001) 8145-8150

Physics

Mathematical Physics

Stylistic changes, English improved and new discussion added

Scientific paper

10.1088/0305-4470/34/39/313

It is shown that the Lame's equation ${d^{2}\over d z^{2}}X+\kappa^{2}
cn^{2}(z, {1\over \sqrt 2})X=0$ can be reduced to the hyper-geometric equation.
The characteristic exponents of this equation are expressed in terms of
elementary functions of the parameter $\kappa$. An analytical condition for
parametric amplification is obtained.

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