Given the relation $$ X_n = X_{n-1}g_{n-1} + X_{n+1}g_{n+1} $$ where $g_{n}$ is some function of $n$, say $g_n = n$, is there a general method to find solutions for $X_n$? Thank you.
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For general coefficients you won't find simple expressions. For specific cases you might be able to derive a formula. – Lelouch Sep 03 '22 at 13:46
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@Lelouch Thanks. Are there any reference texts that I could take a look at to find out more? – 71m3 Sep 03 '22 at 22:43