Difference between revisions of "Logarithm (multivalued) of the exponential"
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(Created page with "==Theorem== The following formula holds: $$\mathrm{Log}\left( \exp(z) \right) = \{ z +2k\pi i \colon k \in \mathbb{Z}\},$$ where $\mathrm{Log}$ denotes the logarithm (multiv...") |
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The following formula holds: | The following formula holds: | ||
$$\mathrm{Log}\left( \exp(z) \right) = \{ z +2k\pi i \colon k \in \mathbb{Z}\},$$ | $$\mathrm{Log}\left( \exp(z) \right) = \{ z +2k\pi i \colon k \in \mathbb{Z}\},$$ | ||
| − | where $\mathrm{Log}$ denotes the [[logarithm (multivalued)]], $\exp$ denotes the [[exponential]], $\pi$ denotes [[pi]], and $i$ denotes the [[ | + | where $\mathrm{Log}$ denotes the [[logarithm (multivalued)]], $\exp$ denotes the [[exponential]], $\pi$ denotes [[pi]], and $i$ denotes the [[imaginary number]]. |
==Proof== | ==Proof== | ||
Revision as of 20:47, 6 June 2016
Theorem
The following formula holds: $$\mathrm{Log}\left( \exp(z) \right) = \{ z +2k\pi i \colon k \in \mathbb{Z}\},$$ where $\mathrm{Log}$ denotes the logarithm (multivalued), $\exp$ denotes the exponential, $\pi$ denotes pi, and $i$ denotes the imaginary number.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 3.3.1
