Timeline for Vastly different runtime when evaluating $\mbox{}_3 F_2$
Current License: CC BY-SA 4.0
6 events
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| Jul 15, 2022 at 17:10 | comment | added | Michael E2 |
If you want to be evaluating a given function multiple times, then I suggest this: func[x_] = FunctionExpand@ HypergeometricPFQRegularized[{1/2, 3, 2}, {1 - 30, 1 + 30}, x]; with Set (=); then use func[x]. Redefine func[x] when you switch functions. For instance, func[999/1000] // N. One might be worried about numerical precision with this workaround. With your examples, it doesn't seem to matter much.
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| Jul 15, 2022 at 15:39 | comment | added | Patrick.B |
The use of FullSimplify helps a bit, but there is still a huge difference in runtime, that is more and more noticeable for $x$ closer to $1$. Try your suggested code with $x=999/1000$ for example.
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| Jul 15, 2022 at 15:37 | history | edited | Patrick.B | CC BY-SA 4.0 |
added 107 characters in body
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| Jul 15, 2022 at 14:40 | comment | added | Bob Hanlon |
RepeatedTiming[HypergeometricPFQRegularized[{1/2, #, 2}, {1 - 30, 1 + 30}, 99/100] // FullSimplify // N] & /@ Range[3, 1, -1]
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| Jul 15, 2022 at 11:15 | history | edited | Patrick.B | CC BY-SA 4.0 |
edited title
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| Jul 15, 2022 at 10:18 | history | asked | Patrick.B | CC BY-SA 4.0 |