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# This question may use zeta function expansion. watch

1. Calculate the limits
2. (Original post by ElliotWalton)
Calculate the limits
How have you come across this? Are you aware of the Laurent expansion of the zeta function centred at 1?
3. (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?
4. (Original post by ElliotWalton)
So How to calculate it?
Is that a yes or a no?
5. (Original post by RichE)
Is that a yes or a no?
To be honest,I have no ideas
6. (Original post by RichE)
Is that a yes or a no?
I tried to used substitution but it does not work out
7. (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

8. (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?
9. (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.
10. (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?
11. (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
12. (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.
13. (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?
14. (Original post by ElliotWalton)
Do you have idea using Zeta function to get the limits?
See post 10

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