I typed
\begin{gather*}
\frac1{1-x}\sum_{n=1}^\infty\left[H_n^3-3H_nH_n^{(2)}+2H_n^{(3)}-\left(H_n-
\frac1n\right)^3\right.\\
\left.+3\left(H_n-\frac1n\right)\left(H_{n}^{(2)}-\frac1{n^2}\right)-2\left(H_{n}^{(3)}-
\frac1{n^3}\right)\right]x^n
\end{gather*}
and I got this ( ignore the equal sign in the picture)
My question is why the square brackets are different in the size? Thank you.
It's worth placing the two main code chunks from lines 1 and 2 on the same line:
In the first code chunk, the expression
\left(H_n-\frac1n\right)
is raised to the third power -- highlighted in orange in the screenshot posted above.
In contrast, the three \left(...\right) terms in the second chunk do not get squared or cubed. As a result, the single tallest object inside \left[...\right. in line 1 is slightly taller than the single tallest object inside \left. ... \right] in line 2.
The upshot? TeX sees fit to make \left[ in line 1 taller than \right] in line 2.
The remedy? Don't overuse \left and \right. For the two-line equation at hand, I'd use \biggl[ on line 1 and \biggr] on line 2 -- and, clearly, get rid of \right. on line 1 and of \left. on line 2 as they're no longer needed.
