How to expand the series $\dfrac{1}{e^x-1}$
Series expansion for $f(x)=\frac{x}{e^x-1}$
In these topics, I have asked for a way to develop the function $\dfrac{x}{e^x-1}$ into series. I won't do that here. From what I see, this function should not have a Maclaurin series (centered at 0) since the function and its higher derivative remain undefined when x=0. Then what is the name for the series derived from the topics that I mention above. Is it a Laurent series or Puisseux series?