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Series with ArcTan gives wrong answer with Wolfram Language!

Stanislav Apostolov
Posted 4 years ago

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)

enter image description here

I am absolutely sure that the correct answer should be

enter image description here

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

There is a plot of all three functions to demonstrate the issue enter image description here

How to get rid of the problem?

(Attached the notebook with corresponding calculations.)

UPD It is a bug. More obvious issue

enter image description here

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.

Attachments:
test-series-arctan-1.nb
POSTED BY: Stanislav Apostolov
2 Replies
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Please add links to/from MSE x-post.
POSTED BY: Daniel Lichtblau

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
POSTED BY: Christian Neel
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