# Result of Series[expression] is different when I simplify the expression

Fixed in 11.2

I have an expression that I want to expand around a given point, and when I do it without simplifying it gives a different result than when I simplify it beforehand.

Full expression

Tttfinal=1/8 (-1 + x^2) Sqrt[1/((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2)] Sqrt[(
r0^4 (1 - y^2)^2)/((1 - x^2)^4 (2 - y^2))] ((
16 x ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2))/(L (-1 + x^2)^2) + (
1/((-1 + x^2)^3))
Sqrt[((-1 + x^2)^2 ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2))/
r0^2] (-x (-1 + x^2) (-4 x (1 - x^2) + (6 Q^2 x (1 - x^2)^2)/
r0^2 + (r0^2 (-6 x + 4 x^3))/L^2) +
2 (1 + x^2) ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2)) - (1/((-1 + x^2)^2))
x ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (r0^2 (3 - 3 x^2 + x^4))/
L^2) ((4 x Sqrt[(1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2])/
r0 + (Sqrt[((-1 + x^2)^2 ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/
r0^2 + (r0^2 (3 - 3 x^2 + x^4))/L^2))/
r0^2] (x (-1 + x^2) (-4 x (1 - x^2) + (6 Q^2 x (1 - x^2)^2)/
r0^2 + (r0^2 (-6 x + 4 x^3))/L^2) -
2 (1 + x^2) ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2)))/(x (-1 +
x^2) ((1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2)) - (
4 x Sqrt[(1 - x^2)^2 - (Q^2 (1 - x^2)^3)/r0^2 + (
r0^2 (3 - 3 x^2 + x^4))/L^2] (2 - y^2))/(r0 (-2 + y^2))))


with the assumptions:

\$Assumptions =
And[x >= 0, x <= 1, y >= -1, y <= 1, Q > 0, L > 0, r0 > 0]


Result:

Series[Tttfinal, {x, 1, 2}] // Simplify
Series[Tttfinal // Simplify, {x, 1, 2}] // Simplify

SeriesData[x, 1, {
Rational[-1, 4] L^(-2) r0^3 (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[3, 8] L^(-2) r0^3 (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[-3, 8] L^(-2) r0^3 (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[1, 16] L^(-2) r0^(-1) (
13 r0^4 + 8 L^2 (Q^2 + r0^2)) (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[1, 64] L^(-2) r0^(-1) (
32 L^4 + 128 L^2 Q^2 - 15 r0^4) (
2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[1, 128] L^(-2) r0^(-3) (
21 r0^6 + 128 L^2 r0^2 (Q^2 + 2 r0^2) + 32 L^4 (8 Q^2 + 9 r0^2)) (
2 - y^2)^Rational[-1, 2] (-1 + y^2)}, -3, 3, 1]
SeriesData[x, 1, {
Rational[-1, 2] L^(-2) r0^(-1) (
r0^4 + L^2 (Q^2 + r0^2)) (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[1, 2] (L^2 - 4 Q^2)
r0^(-1) (2 - y^2)^Rational[-1, 2] (-1 + y^2),
Rational[1, 4]
r0^(-3) ((-4) Q^2 r0^2 + 8 r0^4 + L^2 (8 Q^2 + 9 r0^2)) (
2 - y^2)^Rational[-1, 2] (-1 + y^2)}, 0, 3, 1]


To be clear, the result I expect to be correct is the one where I simplify the expression.

• Your expression for Tttfinal is missing some brackets. – mmeent Sep 5 '17 at 15:00
• How do you know the two results are not equivalent? – m_goldberg Sep 6 '17 at 0:14
• how can they be equivalent? they are series with different coefficients. sorry i will edit with the correct expression – Miguel Oliveira Sep 6 '17 at 15:41
• I am not able to replicate the result indicated above. – Daniel Lichtblau Sep 6 '17 at 16:31
• Okay, I see it now. Adding the "bugs" tag. It's been fixed for a future release though. – Daniel Lichtblau Sep 6 '17 at 20:37

res1=Series[Tttfinal,{x,1,2}]//Normal//Simplify