Difference between revisions of "Relationship between logarithm (multivalued) and positive integer exponents"
From specialfunctionswiki
| Line 6: | Line 6: | ||
==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of a quotient is a difference of logarithms|next=Relationship between logarithm and positive integer exponents}}: 4.1.10 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of a quotient is a difference of logarithms|next=Relationship between logarithm and positive integer exponents}}: $4.1.10$ |
Revision as of 17:26, 27 June 2016
Theorem
Let $z \in \mathbb{C}$ and $n$ be a positive integer. Then the following formula holds: $$\mathrm{Log} \left( z^n \right) \subset n \mathrm{Log}(z),$$ where $\mathrm{Log}$ denotes the logarithm (multivalued) and $n \mathrm{Log}(z)=\left\{nw \colon w \in \mathrm{Log}(z)\right\}$.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.10$
