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### How to memoize with patterns? [duplicate]

Here is an artificial example to explain what I am up to. Define ClearAll[f] f[x_, y_] := f[x, y] = If[x == 0, g[y], g[f[x - 1, y]]] Then ...
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### Functions that remember some arguments while not remembering other arguments

I would like to some programming that is very generic. Particularly I am interested in the following: Let's say I want to write a function ...
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### How to implement a numerically efficient Airy Zeta Function

Define the Airy zeta function for $n=2,3,\dots$, by $$Z(n) := \sum_r \frac{1}{r^n}.$$ where the sum is over the zeros $r$ of the Airy function $\operatorname{Ai}$. In Mathematica the \$\operatorname{...