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Title: Frobenius Method -- from Wolfram MathWorld

Open Graph Title: Frobenius Method -- from Wolfram MathWorld

X Title: Frobenius Method -- from Wolfram MathWorld

Description: If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in the Maclaurin series y=sum_(n=0)^inftya_nx^n. (1) Plug y back into the ODE and group the coefficients by power. Now, obtain a recurrence relation for the nth term, and write the series expansion in terms of the a_ns. Expansions for the first few derivatives are y = sum_(n=0)^(infty)a_nx^n (2) y^' =...

Open Graph Description: If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in the Maclaurin series y=sum_(n=0)^inftya_nx^n. (1) Plug y back into the ODE and group the coefficients by power. Now, obtain a recurrence relation for the nth term, and write the series expansion in terms of the a_ns. Expansions for the first few derivatives are y = sum_(n=0)^(infty)a_nx^n (2) y^' =...

X Description: If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in the Maclaurin series y=sum_(n=0)^inftya_nx^n. (1) Plug y back into the ODE and group the coefficients by power. Now, obtain a recurrence relation for the nth term, and write the series expansion in terms of the a_ns. Expansions for the first few derivatives are y = sum_(n=0)^(infty)a_nx^n (2) y^' =...

Opengraph URL: https://mathworld.wolfram.com/FrobeniusMethod.html

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DC.TitleFrobenius Method
DC.CreatorWeisstein, Eric W.
DC.DescriptionIf x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in the Maclaurin series y=sum_(n=0)^inftya_nx^n. (1) Plug y back into the ODE and group the coefficients by power. Now, obtain a recurrence relation for the nth term, and write the series expansion in terms of the a_ns. Expansions for the first few derivatives are y = sum_(n=0)^(infty)a_nx^n (2) y^' =...
DC.Date.Modified2008-03-14
DC.Subject65L
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/FrobeniusMethod.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2008-03-14
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