Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

We can use the Frobenius method for an ODE like $$u'' + qu = 0$$ where the coefficients are functions if $q$ has a particular negative power series expansion. This is when we take infinity as a regular singular point. In this case, if the indicial equation gives us roots that integer difference, how do we write the solutions? In the case where we expand around 0, we have a term including $\ln(x)$ -- what happens in the infinity case?

share|cite|improve this question

First you make the substitution $x\to\frac{1}{z}$, transform the ODE to the one in the variable $z$, and get a solution $y(z)$ which contains some $\ln(z)$. Then you just substitute back $z\to\frac{1}{x}$ and get terms with $\ln\frac{1}{x}$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.