Titlebook: Differential Equations and Group Theory from Riemann to Poincare; Jeremy Gray Book 19861st edition Birkh?user Boston 1986 ordinary differe

神秘

Algebraic Solutions to a Differential Equation,to solve it for 3rd and 4th order equations, thus providing the first successful treatment of the higher order cases, and to prove a general finiteness theorem for the n. order case (Jordan’s finiteness theorem). Later Fuchs and Halphen were able to treat some of these cases invariant-theoretically.

施加

Modular Equations,o this chapter looks first at Fuchs’s study of elliptic integrals as a function of a parameter, and then at the work of Dedekind. The algebraic study of the modular equation is then discussed, and the chapter concludes with Klein’s unification of these ideas.

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