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I was pleased to see that a recurrence relation that I'm interested in already has been discussed in this MSE post. However I do not understand how to use the function $f(x)$ once all the integration has been completed.

I wish I could make this post longer and discuss what I've tried and where I'm stuck, but I simply have no clue how the make use of $f$. My only idea is that perhaps it can be used to convert the problem into a linear homogenous recurrence relation, but that's just a hunch at this point.

NNN
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1 Answers1

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If

$$f(x)=\sum_{n=0}^{\infty}y_{n}x^n,$$

then the $n$th term of the sequence, $y_n$ is the coefficient of $x^n$ in $f(x)$.

By calculating $f(x)$ as a power series in $x$, then you get all of the terms in the sequence satisfying the recurrence relation.

John
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