Series for log(z) for Re(z) greater than 0

Theorem

The following formula holds for $\mathrm{Re}(z) \geq 0, z \neq 0$: $$\log(z) = 2 \displaystyle\sum_{k=1}^{\infty} \left( \dfrac{z-1}{z+1} \right)^k \dfrac{1}{k},$$ where $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.27$