Timeline for Nature of function as $x\rightarrow\infty$
Current License: CC BY-SA 4.0
24 events
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| Mar 2, 2022 at 7:25 | comment | added | TPC | @JorgeZuniga thank you for the comment sir. I really want to know it's nature as x tends to infinity . I'm unable to do so ,as you have mentioned, it oscillates wildly past some point so asked here if there's an analytic way to show it's nature | |
| Mar 1, 2022 at 15:08 | comment | added | Jorge Zuniga | A short comment. The nature of the $I(x)$ depends on the nature of the integrand's numerator $Im[F(x+iy)-F(x-iy)]$. For x passing some point beyond the (first?) zero of I(x) the integrand behaves wildly. You can plot it. Working with Pari/GP the breakpoint is $x_0=3.208917736262569989928994080...$ for which $I(x_0)=0$. I think Abel-Plana is not a good tool for summation/integration of such kind of functions. You should try an adequate variable transformation first. What if $u=\Gamma(x)$?. | |
| Feb 28, 2022 at 22:15 | comment | added | Stefan Kohl♦ | Please be aware that every edit of a question or of one of its answers bumps the thread to the front page. This has happened for this thread already more than 10 times, and this is a nuisance for other users. Please refrain from unnecessary edits to your posts. -- Usually, the vast majority of minor edits can be avoided by writing and proofreading a question or an answer carefully before posting it. | |
| Feb 28, 2022 at 19:29 | history | edited | TPC | CC BY-SA 4.0 | added 62 characters in body |
| Feb 13, 2022 at 8:43 | comment | added | TPC | Got a downvote. If something wrong please mention. | |
| Feb 5, 2022 at 16:47 | history | edited | TPC | CC BY-SA 4.0 | deleted 34 characters in body |
| Jan 14, 2022 at 4:00 | comment | added | TPC | @MateuszKwaśnicki no sir | |
| Jan 13, 2022 at 21:10 | comment | added | Mateusz Kwaśnicki | Isn't this a duplicate of On new (purely analytic) perspective towards theory of prime numbers? | |
| Jan 13, 2022 at 17:44 | history | edited | TPC | CC BY-SA 4.0 | deleted 27 characters in body |
| Jan 12, 2022 at 14:53 | history | edited | TPC | CC BY-SA 4.0 | deleted 34 characters in body |
| Jan 6, 2022 at 8:18 | history | edited | TPC | CC BY-SA 4.0 | added 48 characters in body |
| Jan 6, 2022 at 7:39 | history | edited | TPC | CC BY-SA 4.0 | added 272 characters in body |
| Jan 6, 2022 at 6:02 | history | edited | TPC | CC BY-SA 4.0 | added 61 characters in body |
| Jan 3, 2022 at 15:59 | comment | added | TPC | @ClaudeLeibovici same problem for me here! I asked here with intention that someone here might have an analytic way to analyse this function. | |
| Jan 3, 2022 at 15:35 | comment | added | Claude Leibovici | Tryng different methods for numerical integration, no problem for $0.218 \leq x \leq 3.381$ but outside this range, all of them just explode | |
| Jan 3, 2022 at 13:12 | history | edited | TPC | CC BY-SA 4.0 | added 87 characters in body |
| Jan 2, 2022 at 12:07 | comment | added | TPC | @CarloBeenakker thank you for the edit sir. totally missed it! | |
| Jan 2, 2022 at 11:46 | history | edited | Carlo Beenakker | CC BY-SA 4.0 | missing prefactor $-i$ inserted |
| Jan 1, 2022 at 18:33 | history | edited | TPC | CC BY-SA 4.0 | added 2 characters in body |
| Jan 1, 2022 at 18:25 | comment | added | TPC | @GeraldEdgar it just pops out in my study of Abel plana summation for different test functions. | |
| Jan 1, 2022 at 18:03 | comment | added | Gerald Edgar | Why is this question of interest? | |
| Jan 1, 2022 at 17:44 | history | edited | TPC | CC BY-SA 4.0 | deleted 2 characters in body; edited title |
| Jan 1, 2022 at 15:02 | history | edited | TPC | CC BY-SA 4.0 | added 104 characters in body |
| Jan 1, 2022 at 6:52 | history | asked | TPC | CC BY-SA 4.0 |