2
$\begingroup$

Let $\phi_n(x), \psi_n(x)$ be solution Sturm-Liouville differential equation

$$p(x) y''(x) - 2n p'(x)y'(x)+2n(2n+1)y(x)=0$$ $$\phi_{n}(0)=0, \hspace{3mm} \phi'_{n}(0)=1;$$ $$\psi_{n}(0)=1, \hspace{3mm} \psi'_{n}(0)=0;$$ where p(x) is given.

Question: Is the set $\{\phi_n(x),\psi_n(x)\}_{n=0}^{\infty}$ orthogonal set?

$\endgroup$
1
  • 1
    $\begingroup$ It's not really a well defined question in this form (orthogonal in what space?), but ignoring that, the answer has to be no, for a general $p$. $\endgroup$ Jan 1, 2018 at 21:33

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.