is the legendre equation an example of a frobenius equation?
is not singular at x=0 and thus is not in the form generally suited to the Frobenius Method. Usually equations of the form:
are solved using the Frobenius method. In the case of Legendre's equation, a solution of the form:
is used, that is integer powers whereas the Frobenius method allows for non-integer powers.
I wasn't aware that there was such a thing as a "Frobenius Equation." It is properly referred to as the "method of Frobenius" which can be applied to a wide variety of linear differential equations including Legendre's DE. It may not be the most convenient, in specific cases, but the method is of general applicability.
Legendre's equation is singular at x= 1 and x= -1 and Frobenius' method could be used to find series solutions about those points.
Yep, yep. That's very good. Thank you both for clearing that up for me. Asdf, I request you solve Legendre's equation about one of the singular points using the method of Frobenius (you brought it up). Please provide a complete report with plots by next Monday morning. Oh I could do it, that would be fun. I use big paper for things like that, write very neat, slowly, constantly referring to references in the matter, and take breaks during the process. And if I get stuck, put it up and work on simpler ones preferably some that are already worked out in some text book then a few on my own.
Oh yea, I'd use Mathematica to check my work.
ORZ... taylor series stuff are one annoying pain...
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