Hello,

The infinite series $\displaystyle \ln(1-x)=-\sum_{j=1}^{\infty }\frac{x^j}{j}\: \: \:; \: \: \: -1< x\leq 1$

might also be expressed $\displaystyle -\sum_{j=1}^{\infty }F^{(j)}(x)\: \: \:; \: \: \: -1< x\leq 1$

where $\displaystyle F^{(j)}(x)$ is the jth integral of x, and $\displaystyle F^{(1)}(x)=x$

Again, this series can be expressed in the function $\displaystyle \ln(1-x)$

Now, my question is does there exist a function that expresses the series $\displaystyle -\sum_{j=1}^{\infty }f^{(j)}(x)\: \: \:; \: \: \: -1< x\leq 1$

where $\displaystyle f^{(j)}(x)$ is the jth *derivative* of x?

(...and I guess $\displaystyle \lim_{j \to \infty}f^{(j)}(x)=1$ or something like that)

Thanks