Every second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lam?equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable.
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In mathematics, the "'Riemann sphere "', named after Bernhard Riemann, is a model of the "'extended complex plane "', the complex plane plus a point at infinity.
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Koebe's theorem also implies that any finitely connected bounded region in the plane is conformally equivalent to the open unit disk with finitely many smaller disjoint closed disks removed, or equivalently the extended complex plane with finitely many disjoint closed disks removed.
