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infinite_geometric_series [2016/07/22 15:19]
infinite_geometric_series [2016/07/22 15:20]
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 == q-Integral == == q-Integral ==
-For a function $f$, the q-integral from $0$ to $1$ is defined as+For a function $f$, the q-integral from $0$ to $1$ ("​$z$-integral"​ if we stick to our notation above) ​is defined as
-$\sum_{k=0}^\infty f(z^k)\,​z^k=\dfrac{1}{1-z}\int_0^1 f(s){\mathrm d}_zs$+$\sum_{k=0}^\infty f(z^k)\,​z^k=\dfrac{1}{1-z}\cdot\int_0^1 f(s)\,{\mathrm d}_zs$
 == Related notes == == Related notes ==
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