Timeline for Does AsymptoticSum work with Arithmetical Number Theoretic Functions?
Current License: CC BY-SA 4.0
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| Jun 27, 2020 at 10:24 | vote | accept | nilo de roock | ||
| Apr 8, 2020 at 17:04 | comment | added | user64494 | It should be $$ \underset {n\to\infty} {\text {lim}} n\sin (2\pi\exp (1) n!)$$ and $$ \underset {n\to\infty} {\text {lim}} \sin (2\pi\exp (1) n!)$$ in my above comment. | |
| Apr 8, 2020 at 14:59 | answer | added | TheDoctor | timeline score: 3 | |
| Mar 31, 2020 at 17:18 | history | edited | bbgodfrey |
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| Mar 28, 2020 at 12:37 | comment | added | nilo de roock | Why does not this belong to the tag Functions? | |
| Mar 27, 2020 at 11:09 | comment | added | J. M.'s missing motivation♦ | This sounds like a good suggestion to send to WRI. | |
| Mar 27, 2020 at 11:09 | history | edited | J. M.'s missing motivation♦ |
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| Mar 27, 2020 at 9:49 | history | edited | nilo de roock | CC BY-SA 4.0 |
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| Mar 25, 2020 at 18:43 | comment | added | user64494 | In any case, you raised an important topic. My personal thanks to you. I am neither a specialist in number theory nor a WRI employee. | |
| Mar 25, 2020 at 18:22 | comment | added | nilo de roock | There is quite a body of theory about the asymptotics of Number Theoretic functions which -could- be implemented, Sin does not belong to that class of functions. Are you a Wolfram Engineer? | |
| Mar 25, 2020 at 18:05 | comment | added | user64494 | Your statement "their sums are remarkably regular" does not correspond to reality: not always. Of course, the certain asymptotic properties of arithmetic functions may be implemented in MMA through tables, but that way is not very well. Here is an example of such type implementation: version 12.0 knows DiscreteLimit[nSin[2*Pin!*Exp[1],n->Infinity], but fails with a simpler one DiscreteLimit[Sin[2*Pi*n!*Exp[1],n->Infinity]. | |
| Mar 25, 2020 at 16:36 | comment | added | nilo de roock | Yes, arithmetical functions are irregular, BUT: their sums are remarkably regular and have nice corresponding asymptotic functions. - I disagree that they are "hardly" implementable. | |
| Mar 25, 2020 at 15:52 | comment | added | user64494 | As a rule, arithmetic functions have irregular behavior so their asymptotic properties are hardly implementable in MMA. | |
| Mar 25, 2020 at 9:42 | history | asked | nilo de roock | CC BY-SA 4.0 |