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Hello

I'm currently investigating the differential equation

$$f''=\left(\sum a_n x^n\right)f$$

I was wondering if anyone could please provide me with a lead as to where I may find the Green's functions? Sadly I have not been able to achieve the result through my own computations

edited May 10 2011 at 7:53

asked Feb 7 2011 at 15:19

backstoreality
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What is a Green's function of a function? – Andrey Rekalo Feb 7 2011 at 16:08

It's the Green's function of a differential equation. Sorry, I will edit that in :) – backstoreality Feb 7 2011 at 17:01

This looks like it ought to yield to a standard application of Sturm-Liouville theory as soon as you make it clear what you want (for instance, what boundary conditions are you interested in?), and there are many e.g. "mathematical physics" textbooks which cover this subject. – jc Feb 7 2011 at 22:17

mathphysicist · Accepted Answer · 2011-02-07 22:33:15Z UTC

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This is indeed fairly standard. Using the two linearly independent solutions to your ODE that you already have you can just follow the procedure outlined e.g. here to construct the Green function.

answered Feb 7 2011 at 22:33

mathphysicist
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Thank you for the link. The original notes that I had were apparently wrong! – backstoreality Feb 8 2011 at 7:23

Green’s Functions

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