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Results tagged with asymptotics
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user 21917
Asymptotic behavior of functions, asymptotic series and related topics
2
votes
2
answers
157
views
Zeros of partial sums of $(1+z)/(1-z)$ near $z=-1$
Is there another approach we could use to find the asymptotics of these zeros near $z=-1$? …
- 224
8
votes
Accepted
Asymptotic expansion of $\zeta(s \mid a,b)= \sum_{n=1}^{\infty} \frac{1}{(n+a)^{s}(n+b)}$
For $s > 0$ we have
$$
\sum_{n=1}^{\infty} \frac{1}{(n+a)^s(n+b)} - \sum_{n=1}^{\infty} \frac{1}{(n+a)^{s+1}} = \sum_{n=1}^{\infty} \frac{a-b}{(n+a)^{s+1}(n+b)} =: g(s).
$$
The series on the right-h …
- 224