Timeline for Infinite sum and product associated with the Weierstrass elliptic function
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Aug 8, 2018 at 17:30 | history | edited | Somos | CC BY-SA 4.0 |
Added more words. Fixed typo. w_1 -> \omega_1.
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| Sep 4, 2017 at 21:43 | vote | accept | Fareeda | ||
| Sep 3, 2017 at 4:06 | comment | added | Somos | Because $Q_0Q_3=\prod_{n>0} (1-q^n),$ and $Q_1Q_2=\prod_{n>0} (1+q^n)$. Thus, $(Q_0Q_3)(Q_1Q_2)^2=(Q_0/Q_3)(Q_1Q_2Q_3)^2$ and since $1=Q_1Q_2Q_3$ we get $Q_0/Q_3$. | |
| Sep 3, 2017 at 3:27 | comment | added | Fareeda | $ \theta_2^2(\sqrt{q })/2= 2 q^\frac{1}{4} \prod \limits_{n=1}^{\infty} (1-q^{n})^2 (1+q^{n})^4 $ how $ \theta_2^2(\sqrt{q })/2=2 q^\frac{1}{4}\prod \limits_{n=1}^{\infty} (1-q^{2n})^2/(1-q^{2n-1})^2$ | |
| Sep 3, 2017 at 3:27 | comment | added | Somos | @Fareeda There are slight differences in reference sources. My sources use $(e_1-e_3)=(\pi/\omega_1)^2\theta_3^4$. The important things is to be consistent. The numbering of the roots $e_1,e_2,e_3$ is a convention. | |
| Sep 3, 2017 at 2:48 | history | edited | Somos | CC BY-SA 3.0 |
Actually I was right the first time.
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| Sep 3, 2017 at 2:35 | comment | added | Fareeda | $(e_1-e_3)= (\frac{\pi}{2\omega_1})^2 \theta_3^4 $ by Abramowitz and I could not find standard identities between theta functions and infinite products, could you please explain me in details how $(e_1 - e_3)(e_2 -e_3)= \theta_2^8$. | |
| Sep 3, 2017 at 2:30 | history | edited | Somos | CC BY-SA 3.0 |
Added more info about theta2*theta3.
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| Sep 3, 2017 at 2:15 | history | edited | Somos | CC BY-SA 3.0 |
add a few words.
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| Sep 2, 2017 at 11:28 | history | edited | Somos | CC BY-SA 3.0 |
Added info about Q_0,...
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| Sep 1, 2017 at 20:01 | history | edited | Somos | CC BY-SA 3.0 |
had to use $$Q_0...$$ instead of inline.
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| Sep 1, 2017 at 19:54 | history | edited | Somos | CC BY-SA 3.0 |
()->[]
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| Sep 1, 2017 at 19:29 | history | edited | Somos | CC BY-SA 3.0 |
Added formulas for Q_0,..., e_1,...
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| Sep 1, 2017 at 18:59 | history | edited | Somos | CC BY-SA 3.0 |
mention middle product.
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| Sep 1, 2017 at 18:29 | comment | added | reuns | There is also some form of the Jacobi triple product involved in the middle step | |
| Sep 1, 2017 at 13:51 | history | edited | Somos | CC BY-SA 3.0 |
rewrite \theta_2 definition
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| Sep 1, 2017 at 13:36 | history | edited | Somos | CC BY-SA 3.0 |
Fixed my typo.
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| Sep 1, 2017 at 13:26 | history | answered | Somos | CC BY-SA 3.0 |