Talk:Frobenius method

00:32, 21 April 2015 (UTC)Hi All,

Firstly, at this time the algebra in this article doesn't make sense. I am sorry but it doesn't. Look at the moment when $I(r)$ was introduced. How did $p(z)$ and $q(z)$ turned into $p(k-j)$ and $q(k-j)$. This doesn't make sense since large integers might not be in the domain of $p$ and $q$

Secondly, when something is being substituted into an ODE, the righthand side must be preserved. i.e. the equation must look like $...=0$. --Resonance cascade (talk) 23:21, 14 November 2008 (UTC)

---

—Preceding unsigned comment added by Resonance cascade (talk • contribs) 23:16, 14 November 2008 (UTC)

In the example, after the phrase "Substitute..." shouldn't the substitution for f' be +SUM... in stead of -SUM... ? no check what you are substituting z^2f"-2zf'+(1-z)f

After dividing by z^2, there should be a z^2 on the bottom of the third term? misprint? no check your algebra (1-z)/(z^2) = 1/z^2 - 1/z

Are you sure the indicial polynomial has p(0) and q(0) instead of p(z) and q(z)? The latter looks like the logical next step from the equations, and it's closer to how I learnt it. Twin Bird 19:41, 17 March 2006 (UTC)

Do not revert my edits, DBolton made a mistake in his/her last edit, i refixed it.

power series

We must remember that it is erroneous to refer to some of these solutions as power series, but simply infinite series, if we have rational numbers in the exponent — Preceding unsigned comment added by 74.192.91.163 (talk) 03:07, 9 April 2012 (UTC)

Mathematical typo?

Is there an error in line 3 for the working in Explanation: substituting? It looks like k + r should be an exponent. --jmenkus ^[T] 15:24, 28 November 2013 (UTC)

whats about if r1-r2 is in {... -1 0 1 ...}. whats Y2--188.158.85.88 (talk) 16:40, 15 January 2014 (UTC)

Form of DE too specific

The method of Frobenius applies to a greater range of differential equations than the equation at the top of the page would indicate (the coefficient of y" doesn't have to be z^2). The third equation defines the boundary (in a sense) between regular and irregular points at z=0, but anything with lesser powers of z in the denominator of y' and y in standard form can also be solved by this method. And in theory you aren't restricted to polynomials. The general formula should have three functions of z as coefficients of y", y' and y. Then redefine P(z) and Q(z) in terms of those functions after dividing through by the coefficient of y". See for example Zil section 6.3. Regarding Tim Bird's comment, the p(0) and q(0) in the indicial polynomial refer to the first term in the power series expansion of zP(z) and z^2Q(z). DaustBerener (talk) 00:35, 21 April 2015 (UTC)

References

Definitions are missing

Please define z as well as the other variables. In particular, is z a real number or is z in the complex numbers? The reader might understand that z is usually a complex, but the page should be clear about the matter.