You can find old bash source here. In particular I downloaded bash-1.14.7.tar.gz. In the
documentation/bash.txt you will find:
Arithmetic expansion allows the evaluation of an arithmetic expression and the substitution of the result. There are two formats for arithmetic expansion:
The references to
$[ are gone in
doc/bash.html from the bash-doc-2.0.tar.gz download and the
NEWS file mentions that:
$[...] arithmetic expansion syntax is no longer supported, in favor of
$((...)) is also the standard syntax for an arithmetic expansion, but may have been added to the standard later than the original Bash implementation.
$[...] does still seem to work in Bash 5.0, so it's not completely removed.