Timeline for Two conjectural identities involving $\zeta(3)$ and the golden ratio $\phi$
Current License: CC BY-SA 4.0
5 events
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| May 28, 2019 at 7:56 | comment | added | Nemo | Since $2(\arcsin x)^2=\sum_{n\ge 1}\frac{(2x)^{2n}}{n^2\binom{2n}{n}}$ and the integrals $\int \frac{(\arcsin (a x))^2}{x} \, dx$, $\int \frac{(\arcsin a)^2-(\arcsin (a x))^2}{1-x} \, dx$, $\int \frac{(\arcsin a)^2-(\arcsin (a \sqrt{x}))^2}{1-x} \, dx$ according to Mathematica have closed forms in terms of Polylogarithms, the sums $\sum_{n\ge 1}\frac{x^{2n}}{n^3\binom{2n}{n}}$, $\sum_{n\ge 1}\frac{x^{2n}}{n^2\binom{2n}{n}}H_n$,$\sum_{n\ge 1}\frac{x^{2n}}{n^2\binom{2n}{n}}H_{2n}$ also have closed form in terms of Polylogarithms. | |
| May 28, 2019 at 1:39 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Added full reference to the paper
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| May 28, 2019 at 1:38 | comment | added | Zhi-Wei Sun | Not that one. The correct source paper is maths.nju.edu.cn/~zwsun/165s.pdf | |
| May 28, 2019 at 1:01 | comment | added | Matt Cuffaro | Is this the source paper? maths.nju.edu.cn/~zwsun/153p.pdf | |
| May 27, 2019 at 23:41 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |