Difference between revisions of "Logarithm (multivalued)"
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Revision as of 06:02, 4 June 2016
The (multivalued) logarithm function $\mathrm{Log} \colon \mathbb{C} \rightarrow \mathscr{P}\left( \mathbb{C} \right)$ is defined by $$\mathrm{Log}(z)=\displaystyle\int_1^z \dfrac{1}{t} \mathrm{d}t,$$ where $\mathscr{P} \left( \mathbb{C} \right)$ denotes the power set of $\mathbb{C}$ and where we understand the integral $\displaystyle\int_1^z$ as a contour integral over a path from $1$ to $z$ that does not cross $0$.
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.4
