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- Frobenius_solution_to_the_hypergeometric_equation abstract "In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we use for complicated ordinary differential equations.The solution of the hypergeometric differential equation is very important. For instance, Legendre's differential equation can be shown to be a special case of the hypergeometric differential equation. Hence, by solving the hypergeometric differential equation, one may directly compare its solutions to get the solutions of Legendre's differential equation, after making the necessary substitutions. For more details, please check the hypergeometric differential equation.We shall prove that this equation has three singularities, namely at x = 0, x = 1 and around x = infinity. However, as these will turn out to be regular singular points, we will be able to assume a solution on the form of a series. Since this is a second-order differential equation, we must have two linearly independent solutions.The problem however will be that our assumed solutions may or not be independent, or worse, may not even be defined (depending on the value of the parameters of the equation). This is why we shall study the different cases for the parameters and modify our assumed solution accordingly.".
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- Frobenius_solution_to_the_hypergeometric_equation wikiPageRevisionID "704404335".
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Category:Hypergeometric_functions.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Category:Modular_forms.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Category:Ordinary_differential_equations.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Differential_equation.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Ferdinand_Georg_Frobenius.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Frobenius_method.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Hypergeometric_function.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Linear_independence.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Pochhammer_symbol.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Recurrence_relation.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Regular_singular_point.
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLink Series_(mathematics).
- Frobenius_solution_to_the_hypergeometric_equation wikiPageWikiLinkText "Frobenius solution to the hypergeometric equation".
- Frobenius_solution_to_the_hypergeometric_equation wikiPageUsesTemplate Template:Cite_book.
- Frobenius_solution_to_the_hypergeometric_equation subject Category:Hypergeometric_functions.
- Frobenius_solution_to_the_hypergeometric_equation subject Category:Modular_forms.
- Frobenius_solution_to_the_hypergeometric_equation subject Category:Ordinary_differential_equations.
- Frobenius_solution_to_the_hypergeometric_equation type Type.
- Frobenius_solution_to_the_hypergeometric_equation type Function.
- Frobenius_solution_to_the_hypergeometric_equation type Redirect.
- Frobenius_solution_to_the_hypergeometric_equation type Type.
- Frobenius_solution_to_the_hypergeometric_equation comment "In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we use for complicated ordinary differential equations.The solution of the hypergeometric differential equation is very important.".
- Frobenius_solution_to_the_hypergeometric_equation label "Frobenius solution to the hypergeometric equation".
- Frobenius_solution_to_the_hypergeometric_equation sameAs Q1640931.
- Frobenius_solution_to_the_hypergeometric_equation sameAs Hypergeometrische_Differentialgleichung.
- Frobenius_solution_to_the_hypergeometric_equation sameAs ガウスの微分方程式.
- Frobenius_solution_to_the_hypergeometric_equation sameAs m.03y0d8h.
- Frobenius_solution_to_the_hypergeometric_equation sameAs Q1640931.
- Frobenius_solution_to_the_hypergeometric_equation wasDerivedFrom Frobenius_solution_to_the_hypergeometric_equation?oldid=704404335.
- Frobenius_solution_to_the_hypergeometric_equation isPrimaryTopicOf Frobenius_solution_to_the_hypergeometric_equation.