The expansion of a logarithmic function, such as loge(1+x), i.e. x − x2/2+x3/3 −…+(−1)nxn/n, or loge(1 − x), i.e. −x − x2/2 − x3/3 − … − xn/n.
Mathematics
The power series
For−1< x ≤ 1 the series converges to ln(1 + x). For x a complex number, with |x| ≤ 1 and x ≠−1, the series converges to a branch of log(1 + x), where log denotes the complex logarithm.