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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

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What is a Green's function of a function? – Andrey Rekalo Feb 7 '11 at 16:08
It's the Green's function of a differential equation. Sorry, I will edit that in :) – backstoreality Feb 7 '11 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. – j.c. Feb 7 '11 at 22:17
up vote 2 down vote accepted

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.

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Thank you for the link. The original notes that I had were apparently wrong! – backstoreality Feb 8 '11 at 7:23

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