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
Domain: mathworld.wolfram.com
| DC.Title | Frobenius Method |
| DC.Creator | Weisstein, Eric W. |
| DC.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^' =... |
| DC.Date.Modified | 2008-03-14 |
| DC.Subject | 65L |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/FrobeniusMethod.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2008-03-14 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_FrobeniusMethod.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_FrobeniusMethod.png |
| None | ie=edge |
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