Você pode obter essas informações em sua máquina local pesquisando $( na página man do Bash:
tomas@tomas-Latitude-E4200:~$ man bash | grep -A2 -B2 '$('
If value is not given, the variable is assigned the null string. All values undergo tilde expansion, parameter and variable expansion, command sub‐
stitution, arithmetic expansion, and quote removal (see EXPANSION below). If the variable has its integer attribute set, then value is evaluated as
an arithmetic expression even if the $((...)) expansion is not used (see Arithmetic Expansion below). Word splitting is not performed, with the
exception of "$@" as explained below under Special Parameters. Pathname expansion is not performed. Assignment statements may also appear as argu‐
ments to the alias, declare, typeset, export, readonly, and local builtin commands. When in posix mode, these builtins may appear in a command
--
Command substitution allows the output of a command to replace the command name. There are two forms:
$(command)
or
'command'
Bash performs the expansion by executing command and replacing the command substitution with the standard output of the command, with any trailing
newlines deleted. Embedded newlines are not deleted, but they may be removed during word splitting. The command substitution $(cat file) can be
replaced by the equivalent but faster $(< file).
When the old-style backquote form of substitution is used, backslash retains its literal meaning except when followed by $, ', or \. The first
backquote not preceded by a backslash terminates the command substitution. When using the $(command) form, all characters between the parentheses
make up the command; none are treated specially.
--
Arithmetic expansion allows the evaluation of an arithmetic expression and the substitution of the result. The format for arithmetic expansion is:
$((expression))
The old format $[expression] is deprecated and will be removed in upcoming versions of bash.
Pode ser necessário algum ajuste para os parâmetros -A e -B . Eles definem o contexto anterior e posterior e dependem da própria página man , do conteúdo e da exibição do terminal - quantos caracteres são exibidos por linha. Então você precisa ver o que vê e pensar no que quer ver.
Mas o resultado pode ser gratificante. Este é o trecho-chave da primeira listagem:
Command substitution allows the output of a command to replace the command name. There are two forms:
$(command)
or
'command'