Ramanujan's integral is ridiculous!

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[maths_]

Correction: around the 7:15 mark I forgot to switch the limits of integration to cancel out the negative sign. Apologies.

[raghavgoyal]

Amazing result. Ramanujan was a genius

[slappy]

At 8:52 you can't just split marked integral into two, since both are infinite and you obtain indeterminate form "infinity minus infinity". The problem disappears if you replace the integral from 0 to alpha^2 with lim_{ epsilon -> 0+ } integral from epsilon to alpha^2 .

[StillOriginalrtcd]

This guy makes an integral equation sounds like u. Love it!!!!

[MrWael]

At minute 8:59, you have to switch the limits of integration to be able to do the next step. So, the first integral should have negative sign. Thank you for your effort.

[pietroantonioli]

9:45 When you split integral from 0 to alfa2 in integrals from 0 to 1 and 1 to alfa2 you imply alpha2>1 but this is not per se guaranteed. You told just alpha>0. Is this derivation still valid if alpha<1?

[deep]

Sir, you split the limit from 0 to (alpha)^2 into limit from 0 to 1 and 1 to (alpha)^2. But alpha>0 its not necessary that it is greater than 1. Can we actually insert 1 like that between limits? 9:40

[subodhkumardhirhe]

incredible result...ramanujan was really a genius

[angelmendez-rivera]

8:26 - 8:29 No, you cannot do that, because two integrals you are trying to split it into diverge.

[anupamamehra]

hi maths 505: so are you planning to make a video on proving zeta(4)=pi^4/90? thanks for your time.

[neilgerace]

8:59 Can we do that? In the first integral the bounds are the wrong way around. What have I missed?

[manstuckinabox]

5:40 darn that's one isomorphic accent, great vid as always my friend.

[fasihullisan]

9:04 integral from infinity to alpha square plus integral from zero to alpha square= integral from zero to infinity, which law is this sir?

[matthaiosghanim]

@ t=5:30, you integral representation of the Euler constant is incorrect. Punch that into the calculator.

[ruffifuffler]

Does this mean genetics is indeterminate after 69 generations?

[tiripoulain]

int_0^{alpha^2} (1/z) does not make sense

[abdoshaat]

How you give z 2 identities in one integral

[DrunkenCArtist]

The solution you presented was by ramanujan himself? Where was it published?