Timeline for Prove that the real part of this limit converges to $\frac{1}{2}$
Current License: CC BY-SA 4.0
10 events
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| Jul 31, 2023 at 15:38 | comment | added | Mats Granvik | Related: math.stackexchange.com/q/4745050/8530 | |
| Jul 30, 2023 at 18:21 | comment | added | Mats Granvik |
"Mathematica start" Clear[s, A, B, n, z, k]; n = 100; s = (1/3 + 14*I); A = Sum[(-1)^(k - 1)*Binomial[n - 1, k - 1]/Zeta[s + k/n], {k, 1, n}]; B = Sum[(-1)^(k - 1)*Binomial[n - 1, k - 1]/Zeta[s + k/n + 1/n], {k, 1, n}]; {N[s + 1/n + 1/(1 - A/B), n], N[Conjugate[-s - 1/n + 1/(1 - B/A)], n]} "Mathematica end"
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| Jul 26, 2023 at 16:16 | comment | added | Mats Granvik |
"Mathematica start" Clear[s, A, B, n, z, k]; n = 19; Reduce[rho == s + 1/n + 1/(1 - A/B) && s + 1/n + 1/(1 - A/B) == Conjugate[-s - 1/n + 1/(1 - B/A)] && B != 0, Re[rho]] "Mathematica end"
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| Feb 1, 2023 at 20:08 | comment | added | Mats Granvik | See Mathematica code at: chat.stackexchange.com/transcript/message/62894215#62894215 | |
| Feb 1, 2023 at 19:56 | comment | added | Mats Granvik | $$=\lim_{n \rightarrow \infty} \left( \left[ 1- \left( \sum _{-n}^n \frac{(-1)^{k-1} \binom{n-1}{k-1}}{\zeta(\tfrac{k}{n}+s)} \Bigg/ \sum _{-n}^n \frac{(-1)^{k-1} \binom{n-1}{k-1}}{\zeta(\tfrac{k}{n}+s+\tfrac{1}{n})} \right) \right]^{-1} +\frac1n + s \right)$$ | |
| Feb 1, 2023 at 19:56 | comment | added | Mats Granvik | $s=14 i$ $$\lim_{n \rightarrow \infty} \left( \left[ 1- \left( \int _{-n}^{n} \frac{(-1)^{k-1} \binom{n-1}{k-1}}{\zeta(\tfrac{k}{n}+s)} \Bigg/ \int _{-n}^{n} \frac{(-1)^{k-1} \binom{n-1}{k-1}}{\zeta(\tfrac{k}{n}+s+\tfrac{1}{n})} \right) \right]^{-1} +\frac1n + s \right)=$$ | |
| Jan 26, 2023 at 18:03 | history | edited | Mats Granvik | CC BY-SA 4.0 |
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| Nov 24, 2020 at 17:09 | history | edited | Mats Granvik | CC BY-SA 4.0 |
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| Nov 24, 2020 at 16:59 | history | edited | Mats Granvik | CC BY-SA 4.0 |
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| Nov 24, 2020 at 16:54 | history | answered | Mats Granvik | CC BY-SA 4.0 |