# InverseSeries giving incorrect result

Somehow in Mathematica 13.2.0.0, InverSeries generates incorrect results.

Let's look at the following two series that differs from each other by a constant number "$$1$$"

InverseSeries[Series[1 + 1/(2 g) + 2/3 (1/g)^(3/2), {g, \[Infinity], 3}], x]
InverseSeries[Series[1/(2 g) + 2/3 (1/g)^(3/2), {g, \[Infinity], 3}], x]


Both outputs are $$\frac{1}{2 x}+\frac{2 \sqrt{2}}{3 \sqrt{x}}-\frac{8}{9}+\frac{40 \sqrt{2} \sqrt{x}}{27}+O\left(x^1\right)$$

However, this is only correct for the second input, the first output should be $$\frac{1}{2 (x-1)}+\frac{2 \sqrt{2}}{3 \sqrt{(x-1)}}-\frac{8}{9}+\frac{40 \sqrt{2} \sqrt{(x-1)}}{27}+O\left((x-1)^1\right)$$

• Reported as a bug. Feb 8, 2023 at 17:06
• I should add the customary caveat that MSE is not a platform for reporting bugs. So this thread may well be closed. Best to report issues directly, via technical support. Feb 8, 2023 at 17:18
• It is interesting to see that absolutely the same two equal results are produced by Mathematica 5.2 (2005) and 8.0.4 (2011). Why should we consider this as bug reporting? This is just an interesting observation on behavior of current and previous versions of our beloved program. People may ask (and tell) who else sees this behavior and what it means. Why immediately a bug? Feb 8, 2023 at 19:59
• Thanks @DanielLichtblau. Yes I do not expect the problem to be resolved by posting it here but it is not a bug report. I just want to post it here for potential users of InverseSeries in case they encounter the same issue. Feb 8, 2023 at 20:29
• (1) Clearly it is bug reporting. One (well, two) can debate as to what extent it might go beyond that. (2) I might be incorrect in my understanding that this site is not for bug reporting (possibly restrictions on that have been lifted). (3) Yes the bug is quite old. Probably goes back to the introduction of InverseSeries. (4) Given its age, I am amazed that it did not get reported before (I checked our data base for this issue and came up empty). (5) It is fixed in our current development kernel. Feb 9, 2023 at 19:00