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This question may use zeta function expansion.

QQ20170723-214742@2x.pngCalculate the limits
Reply 1
Original post by ElliotWalton
QQ20170723-214742@2x.pngCalculate the limits


How have you come across this? Are you aware of the Laurent expansion of the zeta function centred at 1?
Original post by RichE
How have you come across this? Are you aware of the Laurent expansion of the zeta function centred at 1?
So How to calculate it?
Reply 3
Original post by ElliotWalton
So How to calculate it?


Is that a yes or a no?
Original post by RichE
Is that a yes or a no?


To be honest,I have no ideas
Original post by RichE
Is that a yes or a no?


I tried to used substitution but it does not work out
Reply 6
Original post by ElliotWalton
I tried to used substitution but it does not work out


If it makes sense, then you mind find equation (1) from

https://projecteuclid.org/download/pdf_1/euclid.tjm/1270133547

helpful
Reply 7
Original post by ElliotWalton
I tried to used substitution but it does not work out


Actually thinking further, that link is likely overkill as the answer is Euler's constant - have you come across that?
(edited 6 years ago)
Original post by RichE
Actually thinking further, that link is likely overkill as the answer is Euler's constant - have you come acroos that?


Yes,i use mma to get the answer. It is Eular constant.But i still believed it could be solved by zeta function.
Reply 9
Original post by ElliotWalton
Yes,i use mma to get the answer. It is Eular constant.But i still believed it could be solved by zeta function.


Well that limit is the constant coefficient in the Laurent expansion of the zeta function centred at 1. Does that help?
Original post by RichE
Well that limit is the constant coefficient in the Laurent expansion of the zeta function centred at 1. Does that help?


I still can not get a specific thought
Reply 11
Original post by ElliotWalton
I still can not get a specific thought


It's very hard to help, when you've not shared anything about how you met this limit or the extent of your mathematical background. I don't at the moment even know whether you know what a Laurent expansion is.
Original post by RichE
It's very hard to help, when you've not shared anything about how you met this limit or the extent of your mathematical background. I don't at the moment even know whether you know what a Laurent expansion is.


Do you have idea using Zeta function to get the limits?
Reply 13
Original post by ElliotWalton
Do you have idea using Zeta function to get the limits?


See post 10

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