Timeline for Finding a new level-$7$ pi formula using the relation $j_{7A}(\tau) = \left(\sqrt{j_{7B}(\tau)}+\frac{7}{\sqrt{j_{7B}(\tau)}}\right)^2$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2023 at 0:21 | history | edited | Somos | CC BY-SA 4.0 |
Used latest version of my MMA code. Added link to my MMA answer.
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| Jun 8, 2023 at 11:51 | comment | added | Somos | @TitoPiezasIII Thanks for the edit! I had noticed the symmetry myself, but went with the computer generated recurrences. I think the cause is similar to the symmetry for Somos sequences. | |
| Jun 8, 2023 at 11:08 | vote | accept | Tito Piezas III | ||
| Jun 8, 2023 at 11:03 | comment | added | Tito Piezas III | I added the alternative forms which exhibit some symmetry, and I hope you don't mind. I noticed it first in the level-10 recurrences here, then checked if it was also in the level-7 recurrences you found. Do you know what causes such symmetry? | |
| Jun 8, 2023 at 10:58 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Added alternative forms with more symmetry.
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| May 17, 2023 at 17:13 | comment | added | Somos | @TitoPiezasIII It is very possible to have more than one recurrence relation. I have encountered this for several OEIS sequences where the recurrence relation is a homogeneous polynomial in the sequence values with constant coefficients. A good example is Somos sequences. The Somos-4 sequence has many homogeneous recurrence relations that it satisfies. | |
| May 17, 2023 at 15:34 | comment | added | Tito Piezas III | My interest in looking at the recurrence relations was motivated by the Apery-like sequences found by Zagier. Of a certain form, they depend only on three parameters $a,b,c$. Cooper found a more general form with additional parameter $d$, and this enabled him to find the level-$7$ and level-$18$ pi formulas. I believe they are now checking for patterns in 4-term recurrence relations. | |
| May 17, 2023 at 14:54 | comment | added | Tito Piezas III | Wait, this is getting interesting. It is possible for a sequence to have more than one recurrence relation? Let $R(k,n)$ be a $k$-term recurrence with polynomial coefficients of deg-$n$. So the second sequence has at least three, namely $R(6,4)$, $R(8,3)$ by Somos and $R(5,6)$ by G.Edgar? | |
| May 17, 2023 at 12:54 | history | edited | Somos | CC BY-SA 4.0 |
Fixed a typo.
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| May 17, 2023 at 12:08 | history | edited | Somos | CC BY-SA 4.0 |
Make one term per line.
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| May 17, 2023 at 11:55 | history | answered | Somos | CC BY-SA 4.0 |