Difference between revisions of "Series for log(z+a) for positive a and Re(z) greater than -a"
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(Created page with "==Theorem== The following formula holds for $a > 0, \mathrm{Re}(z) \geq -a$, and $z \neq -a$: $$\log(z+a) = \log(a) + 2 \displaystyle\sum_{k=0}^{\infty} \left( \dfrac{z}{2a+z}...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1|next=}}: 4.1.29 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1|next=Limit at infinity of logarithm times reciprocal power function is zero}}: 4.1.29 |
Revision as of 07:54, 4 June 2016
Theorem
The following formula holds for $a > 0, \mathrm{Re}(z) \geq -a$, and $z \neq -a$: $$\log(z+a) = \log(a) + 2 \displaystyle\sum_{k=0}^{\infty} \left( \dfrac{z}{2a+z} \right)^{2k+1} \dfrac{1}{2k+1},$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.29
