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Benedict Irwin edited Integration summation.tex
over 9 years ago
Commit id: 2583bc1f9f5f081b4fcdd60ef4527de168418332
deletions | additions
diff --git a/Integration summation.tex b/Integration summation.tex
index e9feaa1..53ec9a9 100644
--- a/Integration summation.tex
+++ b/Integration summation.tex
...
Does there exist an integral that equals $\zeta(s)$...
\begin{equation}
\zeta(s)=\frac{1}{\Gamma(z)}\int_0^\infty \frac{x^{s-1}}{e^x-1}
\dx \; dx \\
\frac{d}{dx}\frac{x^{s-1}}{e^x-1} = \frac{(e^x (s-x-1)-s+1) x^{s-2}}{(e^x-1)^2} \\
\end{equation}