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infinite_geometric_series [2016/07/22 15:19] nikolaj |
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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 == | ||
