Ramanujan's integral is ridiculous!

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[@maths_505]

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

[@aryaghahremani9304]

your accent had a singularity at the second s in substitution

[@angelmendez-rivera351]

I recommend you start working with a script, the calculations already completed beforehand. This way, these mistakes can be avoided.

[@maddog5597]

I agree 100%. It’s very hard to follow when you go down the rabbit hole of sign/algebra errors.@@angelmendez-rivera351

[@raghavgoyal2222]

Amazing result. Ramanujan was a genius

[@ajaypratap4467]

But why do people in India only feel the genius of Indian mathematicians ... there were several outside the Indian subcontinent... praise them as well

[@Maths_3.1415]

​@@ajaypratap4467 bro this video is related to ramanujan's integral Moreover we respect every mathematician

[@godelianconfucianism8184]

@@ajaypratap4467 yes but Ramanujan was one of a kind, his story is unparalleled and his achivements, considering the whole background, are absolutely praiseworthy. And I'm not even indian

[@DendrocnideMoroides]

@@ajaypratap4467 I do not feel the need to only praise and respect people of my country, I will respect anyone respectable.

[@UnknownGhost97]

He is just a normal mathematician he has used this problems for the research outside india

[@slappy1140]

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!!!!

[@pietroantonioli4297]

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

[@subodhkumardhirhe8467]

incredible result...ramanujan was really a genius

[@user-injective]

Omg this is sooo beautiful!

[@MohamedachrafKadim-jm5yr]

❤ nice

[@maths_505]

Thanks bro

[@evolevil1]

nice indeed

[@F-S.]

4:04 so smooth

[@maths_505]

😂😂😂

[@MrWael1970]

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.

[@maths_505]

Yes you're right. I've corrected that in a pinned comment. Thank you professor ☺️

[@anupamamehra6068]

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

[@maths_505]

Will do

[@deep45789]

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

[@neilgerace355]

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

[@maths_505]

Bro just switch their places

[@yoav613]

It should be from a^2 to inf because the - sine du=-a/z^2

[@maths_505]

​@@yoav613oh now I see it! Thanks bro

[@angelmendez-rivera351]

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

[@manstuckinabox3679]

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

[@maths_505]

Thank you comrad ManStuckInABoxovsky

[@Tim-Kaa]

Nice

[@davidst.arnauld6763]

My brain is still spinning!

[@TheJara123]

Wonderfully presented man!!

[@fasihullisan3066]

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?

[@maths_505]

Read the pinned comment😂

[@matthaiosghanim562]

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

[@abdoshaat3304]

How you give z 2 identities in one integral

[@ruffifuffler8711]

Does this mean genetics is indeterminate after 69 generations?

[@tiripoulain]

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

[@jackkalver4644]

True. Two divergent integrals could sum to anything. Perhaps you should’ve combined the integrals first instead of splitting them first.

[@sammtanX]

that accent escalated quickly

[@DrunkenCArtist]

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

[@renerpho]

Not the accent part.

[@DrunkenCArtist]

😂 indeed

[@DrunkenCArtist]

@@renerpho but where did you found that ?can you share the link of first published solution by him ,if it's available

[@omargaber3122]

Really wonderful