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Abstract
To study ∫ 2β 2 ρ/√Q ρdρ and ∫ 2(ρ 4−de)ρdρ/√Q, where Q is a quartic in ρ 2 without the ρ 2 terms, to find the perimeter and the cross section area of the Cassinian wave guide, to finally establish the perturbation theory of this famous waveguide.