[Tex/LaTex] Why use the control sequences \bigl, \biggl, \bigr or \biggr, as I can always use \big or \bigg

delimitersmath-mode

If my manuscript file has

$$\biggl({\partial^2\over \partial x^2}+
   {\partial^2 \over \partial y^2}\biggr)\bigl|\varphi(x+iy)\bigr|^2 = 0$$

or

$$\bigg({\partial^2\over \partial x^2}+
  {\partial^2 \over \partial y^2}\bigg)\big|\varphi(x+iy)\big|^2 = 0$$

the result will be the same :

enter image description here

Best Answer

\big (and its friends) create an Ord(inary) atom. \bigl and \bigr (and their friends) create Open and Close atoms. Spacing between atoms can vary.

For example, TeX inserts a thin space between an Op (big operator) atom and an Ord atom, while it inserts no space between an Op atom and an Open atom.

Compare (Op and then Ord):

\[ \sum\big( \]

with (Op and then Open):

\[ \sum\bigl( \]

You can see the a list of the 13 kinds of atoms in page 158 of the TeXbook. The table in page 170 shows the spacing between pairs of adjacent atoms.

EDIT: In the example give by bellochio, there's no difference in spacing due to the kind of atoms involved in both expressions; the only part which could be considered problematic is the initial part: 

\biggl({\partial^2\over \partial x^2}

versus

\bigg({\partial^2\over \partial x^2}

However, using \showlists for the first expressions produces (only the relevant parts are shown):

### display math mode entered at line 1
\mathopen
.\hbox(14.5001+9.50012)x7.36115
..\mathon
..\hbox(14.5001+9.50012)x7.36115
...\hbox(0.39998+23.60025)x7.36115, shifted -14.10013 []
...\vbox(14.5+0.0)x0.0
...\hbox(0.0+0.0)x0.0, shifted -2.5
..\mathoff
\mathord
.\fraction, thickness = default
.\\mathord
.\.\fam1 @
.\^\fam0 2
./\mathord
./.\fam1 @
./\mathord
./.\fam1 x
./^\fam0 2

so the first atoms are of type Open, and Ord. For the second expression \showlists produces:

### display math mode entered at line 1
\mathord
.\hbox(14.5001+9.50012)x7.36115
..\mathon
..\hbox(14.5001+9.50012)x7.36115
...\hbox(0.39998+23.60025)x7.36115, shifted -14.10013 []
...\vbox(14.5+0.0)x0.0
...\hbox(0.0+0.0)x0.0, shifted -2.5
..\mathoff
\mathord
.\fraction, thickness = default
.\\mathord
.\.\fam1 @
.\^\fam0 2
./\mathord
./.\fam1 @
./\mathord
./.\fam1 x
./^\fam0 2

so the first atoms are of type Ord, and Ord. According to the table in page 170, TeX inserts no space between an Open and an Ord atom and also between two Ord atoms and that's why there's no difference in the spacing.

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