1 - Codeforces

Revision en2, by bfsof123, 2024-05-31 12:01:41

In this blog we will prove a mysterious identity:

$$$\sum\limits_{n1 \in \mathbb{Z}}(-1)^{n1}\sum\limits_{(n_2, n_3) \in \mathbb{Z}^2}\frac{1}{} = 1$$$.

math, modular form, ramanujan, lattice sum, sinh, codeforces

History

Revisions

Rev.	By	When	Δ	Comment
en52	bfsof123	2024-06-18 14:39:37	16
en51	bfsof123	2024-06-06 20:29:14	96
en50	bfsof123	2024-06-03 16:56:18	96
en49	bfsof123	2024-06-02 18:04:42	9	Tiny change: 'n_formula), and the' -> 'n_formula) (Eq.(3)), and the'
en48	bfsof123	2024-05-31 18:09:13	114
en47	bfsof123	2024-05-31 18:03:22	49
en46	bfsof123	2024-05-31 18:02:06	8
en45	bfsof123	2024-05-31 17:52:52	227
en44	bfsof123	2024-05-31 17:41:17	59
en43	bfsof123	2024-05-31 17:35:18	14	Tiny change: '.5)^2})}}$, therefore it is suffi' -> '.5)^2})}}$. It is suffi'
en42	bfsof123	2024-05-31 17:33:31	106
en41	bfsof123	2024-05-31 17:30:25	2	Tiny change: 'm\limits_{0}^\infty ' -> 'm\limits_{n=0}^\infty '
en40	bfsof123	2024-05-31 16:54:54	15	Tiny change: 'the other one comes fro' -> 'the other $\sqrt{\pi}$ comes fro'
en39	bfsof123	2024-05-31 16:17:58	544
en38	bfsof123	2024-05-31 13:48:12	6	Tiny change: 'mathbb{Z}}(-1)^n\exp(\frac' -> 'mathbb{Z}}\exp(\frac'
en37	bfsof123	2024-05-31 13:44:21	49
en36	bfsof123	2024-05-31 13:34:07	13
en35	bfsof123	2024-05-31 13:33:26	30
en34	bfsof123	2024-05-31 13:28:38	441
en33	bfsof123	2024-05-31 13:21:55	1	Tiny change: '3/011/pdf)` with a [s' -> '3/011/pdf) with a [s' (published)
en32	bfsof123	2024-05-31 13:21:05	6	Tiny change: 'h initial data $a_1 := \' -> 'h initial term $a_1 := \' (saved to drafts)
en31	bfsof123	2024-05-31 13:10:42	0	(published)
en30	bfsof123	2024-05-31 13:10:04	26
en29	bfsof123	2024-05-31 13:08:57	5
en28	bfsof123	2024-05-31 13:08:27	490
en27	bfsof123	2024-05-31 13:01:51	1	Tiny change: '=sharing) `[Exact res' -> '=sharing) [Exact res'
en26	bfsof123	2024-05-31 13:00:02	60
en25	bfsof123	2024-05-31 12:59:14	78
en24	bfsof123	2024-05-31 12:58:02	73
en23	bfsof123	2024-05-31 12:57:17	552
en22	bfsof123	2024-05-31 12:51:22	515
en21	bfsof123	2024-05-31 12:46:06	78
en20	bfsof123	2024-05-31 12:45:00	82
en19	bfsof123	2024-05-31 12:43:17	144
en18	bfsof123	2024-05-31 12:38:46	63
en17	bfsof123	2024-05-31 12:37:10	41
en16	bfsof123	2024-05-31 12:36:12	192
en15	bfsof123	2024-05-31 12:33:24	303
en14	bfsof123	2024-05-31 12:28:59	247
en13	bfsof123	2024-05-31 12:26:10	359
en12	bfsof123	2024-05-31 12:24:43	495
en11	bfsof123	2024-05-31 12:19:18	244
en10	bfsof123	2024-05-31 12:15:10	684
en9	bfsof123	2024-05-31 12:13:47	50
en8	bfsof123	2024-05-31 12:12:42	216
en7	bfsof123	2024-05-31 12:08:27	1	Tiny change: '2 + n_4^2}\n\n' -> '2 + n_4^2}$\n\n'
en6	bfsof123	2024-05-31 12:08:17	213
en5	bfsof123	2024-05-31 12:04:54	7
en4	bfsof123	2024-05-31 12:04:10	47
en3	bfsof123	2024-05-31 12:02:56	39
en2	bfsof123	2024-05-31 12:01:41	150
en1	bfsof123	2024-05-31 11:59:11	2	Initial revision (saved to drafts)