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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 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.".
- Frobenius_solution_to_the_hypergeometric_equation wikiPageID "16407499".
- Frobenius_solution_to_the_hypergeometric_equation wikiPageRevisionID "595112012".
- Frobenius_solution_to_the_hypergeometric_equation hasPhotoCollection Frobenius_solution_to_the_hypergeometric_equation.
- 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 Abstraction100002137.
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- Frobenius_solution_to_the_hypergeometric_equation type DifferentialEquation106670521.
- Frobenius_solution_to_the_hypergeometric_equation type Equation106669864.
- Frobenius_solution_to_the_hypergeometric_equation type Form106290637.
- Frobenius_solution_to_the_hypergeometric_equation type Function113783816.
- Frobenius_solution_to_the_hypergeometric_equation type HypergeometricFunctions.
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- Frobenius_solution_to_the_hypergeometric_equation type MathematicalRelation113783581.
- Frobenius_solution_to_the_hypergeometric_equation type MathematicalStatement106732169.
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- Frobenius_solution_to_the_hypergeometric_equation type ModularForms.
- Frobenius_solution_to_the_hypergeometric_equation type OrdinaryDifferentialEquations.
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- Frobenius_solution_to_the_hypergeometric_equation type Relation100031921.
- Frobenius_solution_to_the_hypergeometric_equation type Statement106722453.
- Frobenius_solution_to_the_hypergeometric_equation type Word106286395.
- 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 label "Hypergeometrische Differentialgleichung".
- Frobenius_solution_to_the_hypergeometric_equation label "ガウスの微分方程式".
- 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 sameAs Q1640931.
- Frobenius_solution_to_the_hypergeometric_equation sameAs Frobenius_solution_to_the_hypergeometric_equation.
- Frobenius_solution_to_the_hypergeometric_equation wasDerivedFrom Frobenius_solution_to_the_hypergeometric_equation?oldid=595112012.
- Frobenius_solution_to_the_hypergeometric_equation isPrimaryTopicOf Frobenius_solution_to_the_hypergeometric_equation.