Series acot – bug?

[hp-zl]

All the best in the New Year.

Now to the point.
HP-G2, firmware 2.1.14730 (2023 04 13)
CAS Mode

I type:
series(acot(x),x,0,6)
I receive:
order_size(x)

But it should be:
π/2 - x + x^3/3 - x^5/5

Writing:
series(atan(x),x,∞,6)

I get the correct result:
π/2 - 1/x + (1/x)^3/3 - (1/x)^5/5 + (1/x)^7*order_size(1/x).

Is it only like this for me or also for you?
Regards.

[Nigel (UK)]

Not a bug. acot(x) is discontinuous at x=0 (try plotting it to see this). To get the expansion you want you can use series(acot(x), x, 0, 6, 1) where the final ‘1’ tells the calculator to look for a series valid for x>0.

Nigel (UK)

[hp-zl]

You're right.
I forgot about the fifth argument [Dir] of the series function.
Thanks for the reminder.
Regards.