Timeline for What is the indefinite sum of tan(x)?
Current License: CC BY-SA 2.5
10 events
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| May 27, 2014 at 20:26 | comment | added | thomashennecke | The book of N. E. Nörlund: Vorlesungen über Differenzenrechnung, 1923, reprinted by Chelsea, 1954 credites A. Hurwitz with showing, that a meromorphic sum can be found for any meromorphic right hand side in chapter 3, §1 historical remarks, 18. The work of Hurwitz is cited as "Sur l'integrale finie d'une fonction entiere", Acta math. 20 (1897), p. 285 - 312 and Acta math. 22 (1899), p. 197 - 180. | |
| Dec 29, 2011 at 10:00 | vote | accept | Herman Tulleken | ||
| Oct 21, 2010 at 18:49 | comment | added | Gerald Edgar | Alternatively: note that if you translate by any integer multiple of $\pi$ then you get another solution $T(z+m\pi)$ of the original problem. So the difference between $T(z)$ and this other solution is periodic with period 1. | |
| Oct 21, 2010 at 18:43 | history | edited | Gerald Edgar | CC BY-SA 2.5 |
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| Oct 21, 2010 at 14:28 | comment | added | Herman Tulleken | Indeed, it is easy to prove that $T(z + \pi) - T(z) = -[\Psi(1 - (\pi/2 + z)) -\Psi(\pi/2 + z)] = -\pi \cot \pi(\pi/2 + z)$. | |
| Oct 21, 2010 at 13:08 | comment | added | Herman Tulleken | Yes, thanks for the additional information. Interestingly, it looks like $T(x + \pi) - T(x)$ is also periodic, with period 1. | |
| Oct 21, 2010 at 0:47 | comment | added | J. M. isn't a mathematician | NICE! I have to confess it only became obvious to me only after you wrote the thing out in full. Thanks a lot! | |
| Oct 21, 2010 at 0:42 | history | edited | Gerald Edgar | CC BY-SA 2.5 |
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| Oct 21, 2010 at 0:32 | history | edited | Gerald Edgar | CC BY-SA 2.5 |
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| Oct 21, 2010 at 0:23 | history | answered | Gerald Edgar | CC BY-SA 2.5 |