Taylor Series for $\log(x)$ Does anyone know a closed form expression for the Taylor series of the function $f(x) = \log(x)$ where $\log(x)$ denotes the natural logarithm function?

Abromowitz & Stegun gives a number of forms.
Among these, the bilinear expansion is known for its used in digital filter theory:
$$\log(z) = 2\left[\left({z-1\over z+1}\right)+ {1\over3} \left({z-1\over z+1}\right)^3 + {1\over5} \left({z-1\over z+1}\right)^5+ \cdots\right],$$
for $\Re z > 0.$
Series of log(x)
