Timeline for Possible new series for $\pi$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 20 at 16:22 | comment | added | Yiftach Barnea | In second thought, here is a slightly less stupid idea. Fix g, then integrate from 0 to 1/2, then from 1/2 to 3/4, then from 3/4 to 7/8, and so on. You get a series that depends on g. Again, no idea if it is interesting. | |
| Jul 20 at 16:01 | comment | added | Yiftach Barnea | Thanks, I guess the intuition was right, but its direction was wrong. :-) | |
| Jul 20 at 15:47 | comment | added | Dan Romik | @YiftachBarnea a limit of sums is not always a sum. In this case it’ll be an integral. By the way, the integration identity is proved precisely by starting with a discrete summation identity and taking a limit more or less as you suggest. | |
| Jul 20 at 11:56 | comment | added | Yiftach Barnea | this might be a stupid question (it is far from what I do). But if you take $g$ to be a step function and approximate it with smooth functions and then take the limit shouldn't you get a sum? Then couldn't you increase the number steps and get in the limit a series? Though, I am not sure this is interesting, | |
| Jul 20 at 6:01 | history | answered | Dan Romik | CC BY-SA 4.0 |