Timeline for Asymptotic expansion of $\zeta(s \mid a,b)= \sum_{n=1}^{\infty} \frac{1}{(n+a)^{s}(n+b)}$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2015 at 15:42 | history | edited | Antonio Vargas | CC BY-SA 3.0 |
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| Feb 24, 2015 at 10:49 | vote | accept | Olivier Oloa | ||
| Feb 24, 2015 at 10:47 | comment | added | Olivier Oloa | Thank you Antonio. +1 and accepted. There is a typo in your result, the factor $a-b$ should appear in your expansion. Observe that, using the notations in my previous comment, we get $$\gamma_0(a,b)=-\psi(b+1)$$ due to the classic evaluation $$\sum_{n=1}^\infty \frac{a-b}{(n+a)(n+b)} =\psi(a+1)-\psi(b+1).$$ I'm looking for an 'interesting' evaluation for $\gamma_1(a,b)$. | |
| Feb 24, 2015 at 4:20 | history | edited | Antonio Vargas | CC BY-SA 3.0 |
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| Feb 24, 2015 at 4:12 | review | First posts | |||
| Feb 24, 2015 at 4:17 | |||||
| Feb 24, 2015 at 4:12 | history | answered | Antonio Vargas | CC BY-SA 3.0 |