24 Jun
2023
24 Jun
'23
6:06 p.m.
On 24/06/2023, Richard B. Kreckel <kreckel@in.terlu.de> wrote:
The substitution above is not correct if e<0. For example:
x = Order(1/A) => |x| <= Const * 1/A
but
x = 1/Order(A) => |x| >= 1 / (Const * A)
so
Order(1/A) =/= 1/Order(A)
It is correct for non-negative integer e though.
Wait.
Consider a series which terminates in Order(x^n). We don't make any statement about the magnitude or the sign of the constant in front of the Order(x^n) term. Likewise for Order(x)^n. Hence, I think the transformation Order(x)^n -> Order(x^n) is correct, even if n<0.
Comments or objections?
If a series A starts with x^n, then the series 1/A *ends*, not starts, with 1/x^n.