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/sci/ - Science & Math

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8756292 No.8756292 [Reply] [Original]

Is "1 + 2 + 3 + 4 ..." only associated with -1/12 in the context of the Riemann Zeta Function, or is that series also associated with that number in the context of other analytically continued functions?

If the it's the former case, then isn't analytic continuation just total bollocks?

>> No.8756295

Just because it didn't give you an answer you intuitively expect doesn't mean it's wrong.

>> No.8756304

>>8756295
It's wrong if it's not consistent, which is the point of this question. Do you even know what all the words I said mean?

>> No.8756337

>>8756304
It's you who doesn't know what the words mean if you think analytic continuation might just be 'total bollocks' you brainlet

>> No.8756372
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8756372

>>8756292
The definition of holomorphism is completely reasonable. Nice properties. Makes complex analysis seemingly easier than real analysis. Holomorphic extension is unique by Liouville theorem. The zeta function is the unique answer. Suck it.

>> No.8756375

>>8756292
you're obviously an undergraduate brainlet who's probably never even taken a complex analysis class and apparently can't even use google to see that all methods give -1/12

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF#Summability