Difference between revisions of "Logarithm (multivalued) of product is a sum of logarithms (multivalued)"
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(Created page with "==Theorem== The following formula holds for any $z_1,z_2 \in \mathbb{C}$: $$\mathrm{Log}\left( z_1z_2 \right) \subset \mathrm{Log}(z_1) + \mathrm{Log}(z_2),$$ where $\mathrm{L...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between logarithm (multivalued) and logarithm|next=Logarithm of product is a sum of logarithms}}: 4.1.6 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between logarithm (multivalued) and logarithm|next=Logarithm of product is a sum of logarithms}}: $4.1.6$ |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 17:24, 27 June 2016
Theorem
The following formula holds for any $z_1,z_2 \in \mathbb{C}$: $$\mathrm{Log}\left( z_1z_2 \right) \subset \mathrm{Log}(z_1) + \mathrm{Log}(z_2),$$ where $\mathrm{Log}$ denotes the logarithm (multivalued) and $\mathrm{Log}(z_1) + \mathrm{Log}(z_2)$ denotes the sumset of $\mathrm{Log}(z_1)$ and $\mathrm{Log}(z_2)$.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.6$
