Timeline for Malmsten-like integrals for $\zeta(n) $
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 21 at 21:42 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
Corrected an identity
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| Jul 5 at 13:23 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
added a dx to an integral
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| Jul 5 at 11:31 | comment | added | Max Lonysa Muller | @JorgeZuniga Thank you for the reference, it seems useful and relevant | |
| Jul 5 at 6:15 | comment | added | Jorge Zuniga | $\zeta(n)/\pi^{n-1}$ integrals, $n$ odd, can be found using PSLQ algorithm to get the numerator polynomials $x\,P_{2n-2}(x)$ coefficients with polynomials $Q_{2n+2}(x)=(1+x^2)^{n+1}$ in denominators. For Catalan's Constant $G/\pi$ I think that polynomial $P_2(x)$ should be searched with $Q_6(x)=(1+x^2)^3$. Look at this reference arxiv.org/pdf/0808.2750. I hope it is useful. | |
| Jul 4 at 14:48 | history | edited | Hjalmar Rosengren | CC BY-SA 4.0 |
typo
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| Jul 4 at 12:44 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
fixed an expression for zeta(5)
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| Aug 24, 2022 at 19:18 | comment | added | Max Lonysa Muller | @StevenClark Fair enough, thank you. | |
| Aug 24, 2022 at 19:12 | comment | added | Steven Clark | Yes, but I thought it might be worth mentioning since the integration range is the same and the answer below seems to imply there are no Malmsten-like integral for even values. | |
| Aug 24, 2022 at 19:01 | comment | added | Max Lonysa Muller | @StevenClark Interesting, thank you. Yet these are not Malmsten integrals of the form described in $(1)$ above, right? | |
| Aug 24, 2022 at 18:34 | comment | added | Steven Clark | An integral representation for even positive integers is given by $\zeta(2 n)=\frac{(-1)^{n+1} 2^{2 n-3} \pi ^{2 n}}{\left(2^{2 n}-1\right) (2 n-2)!} \int\limits_0^1 E_{2 n-2}(x) \, dx$ where $E_n(x)$ is an Euler Polynomial (see mathworld.wolfram.com/EulerPolynomial.html). | |
| Aug 24, 2022 at 15:12 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
Fixed a small error in a sentence
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| Aug 16, 2022 at 22:21 | answer | added | Henri Cohen | timeline score: 9 | |
| Aug 16, 2022 at 20:13 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
fixed an equation
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| Aug 16, 2022 at 19:22 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
forgot a word in a sentence, fixed it
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| Aug 16, 2022 at 19:16 | history | asked | Max Lonysa Muller | CC BY-SA 4.0 |