Log expansions

There are many series for Log[x] but generally they only cover a very small range of x.

This might be useful: http://functions.wolfram.com/ElementaryFunctions/Log/06/01/01/

 

The series expansion of any function can be obtained by Taylor's series expansion:
f(x)=f(a)+(x-a)f'(a)+(x-a)^2f"(a)/2!+(x-a)^3f"'(a)/3!+...

Using the above formula, any function can be expanded in terms of powers of (x-a), provided that all derivatives of f(x) are defined at x=a.

Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.

 

From a Yahoo search on Logarithmic Expansion:

http://www.math2.org/math/expansion/log.htm

 

I think you mean log x cannot be expanded about zero in a series of nonnegative powers.

 

example can be done via the log(1+x) series |x|<1

x-x^2/2+x^3/3....