Series with ArcTan gives wrong answer with Wolfram Language!

Questions
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1

Hi!
Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression!

When calculating

Series[ArcTan[A + 1/x], {x, 0, 2}, Assumptions -> A > 0 && x > 0]

Wolfram Language returns the wrong answer (tested in Wolfram cloud and in Mathematica 12.1.1.0)

Screenshotat2021-03-0417-53-25.png

I am absolutely sure that the correct answer should be

Screenshotat2021-03-0417-54-33.png

(I have a Ph.D. degree and teach for many years.)

There is a plot of all three functions to demonstrate the issue

Screenshotat2021-03-0417-57-32.png
Screenshotat2021-03-0417-57-32.png512×585 26.8 KB

How to get rid of the problem?

(Attached the notebook with corresponding calculations.)

UPD It is a bug. More obvious issue

Screenshotat2021-03-0422-07-07.png
Screenshotat2021-03-0422-07-07.png585×420 18.6 KB

UPD#2 Working around.

The result in v10.3 is correct.

The result in v11.3 is incorrect.

The corresponding post is in Mathematica Stackexchange.

test-series-arctan-1.nb (25.3 KB)

2

I tested the example

Series[ArcTan[A + 1/x], {x, 0, 2},  Assumptions -> A > 0 && x > 0]

on two versions of Mathematica:

  1. with Mathematica 9.0.1.0 : I get answer Pi/2 - x + A x²+…
  2. with Mathematica 12.1.1 : I get the answer Pi/2 - x + (A +A² Pi/4) x²+…
    So I reproduce your observation. I tested the old version on Win Xp (!) and the new on Win7 each time from a fresh Kernel.

Rgds

Christian

3

Please add links to/from MSE x-post.