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Casimir energy of a compact cylinder under the condition<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ɛ</mml:mi><mml:mi>μ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>=</mml:mo><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>
The Casimir energy of an infinite compact cylinder placed in a uniform unbounded medium is investigated under the continuity condition for the light velocity when crossing the interface. As a characteristic parameter in the problem the ratio ${\ensuremath{\xi}}^{2}=({\ensuremath{\varepsilon}}_{1}\ensuremath{-}{\ensuremath{\varepsilon}}_{2}{)}^{2}/({\ensuremath{\varepsilon}}_{1}+{\ensuremath{\varepsilon}}_{2}{)}^{2}=({\ensuremath{\mu}}_{1}\ensuremath{-}{\ensuremath{\mu}}_{2}{)}^{2}/({\ensuremath{\mu}}_{1}+{\ensuremath{\mu}}_{2}{)}^{2}<~1$ is used, where ${\ensuremath{\varepsilon}}_{1}$ and ${\ensuremath{\mu}}_{1}$ are, respectively, the permittivity and permeability …