Difference between revisions of "Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued)"
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(Created page with "==Theorem== Let $z_1,z_2 \in \mathbb{C}$ with $z_2 \neq 0$. The following formula holds: $$\mathrm{Log} \left( \dfrac{z_1}{z_2} \right) \subset \mathrm{Log}(z_1) - \mathrm{Log...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of product is a sum of logarithms|next=Logarithm of a quotient is a difference of logarithms}}: 4.1.8 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of product is a sum of logarithms|next=Logarithm of a quotient is a difference of logarithms}}: $4.1.8$ |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 17:26, 27 June 2016
Theorem
Let $z_1,z_2 \in \mathbb{C}$ with $z_2 \neq 0$. The following formula holds: $$\mathrm{Log} \left( \dfrac{z_1}{z_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 difference set 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): $4.1.8$
