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I wanted to ask if anyone knows of good texts/resources on methods for solving holonomic recurrence relations (if there are any general analytical approaches): $$p_1(n)a(n)+p_2(n)a(n-1)+\dotsb+p_k(n)a(n-k+1) = 0,\quad \text{$p$ a polynomial in $n$}.$$

Only analytical approach I can find online is when we have a non-homogeneous two-term equation and can apply the method of summation factor.

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    $\begingroup$ A couple of such recurrences appear in Apery's celebrated proof (see A proof that Euler missed by Poorten), and their solutions don't have closed-form expressions but only representations as certain sums. $\endgroup$
    – Max Alekseyev
    Commented Feb 15, 2023 at 1:38

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