Fuchs' theorem

Fuchs' theorem (Redirected from Fuchs's theorem) Jump to navigation Jump to search This article includes a list of references, lecture connexe ou liens externes, mais ses sources restent floues car il manque de citations en ligne. Merci d'aider à améliorer cet article en introduisant des citations plus précises. (Juin 2017) (Découvrez comment et quand supprimer ce modèle de message) En mathématiques, Fuchs' theorem, named after Lazarus Fuchs, states that a second-order differential equation of the form {displaystyle y''+p(X)y'+q(X)y=g(X)} has a solution expressible by a generalised Frobenius series when {style d'affichage p(X)} , {style d'affichage q(X)} et {style d'affichage g(X)} are analytic at {style d'affichage x=a} ou {style d'affichage a} is a regular singular point. C'est-à-dire, any solution to this second-order differential equation can be written as {displaystyle y=sum _{n=0}^{infime }un_{n}(x-a)^{n+s},quad a_{0}neq 0} for some positive real s, ou {displaystyle y=y_{0}dans(x-a)+somme _{n=0}^{infime }b_{n}(x-a)^{n+r},quad b_{0}neq 0} for some positive real r, where y0 is a solution of the first kind.

Its radius of convergence is at least as large as the minimum of the radii of convergence of {style d'affichage p(X)} , {style d'affichage q(X)} et {style d'affichage g(X)} .

See also Frobenius method References Asmar, Nakhlé H. (2005), Partial differential equations with Fourier series and boundary value problems, Upper Saddle River, New Jersey: Pearson Prentice Hall, ISBN 0-13-148096-0. Butkov, Eugène (1995), Mathematical Physics, En lisant, MA: Addison-Wesley, ISBN 0-201-00727-4. Catégories: Differential equationsTheorems in analysis