my $DIR;
$DIR = '\\ax-risvis447\c$\calc';
print $DIR;  # prints "\ax-risvis447\c$\calc"

# This gets you the string you want:
$DIR = '\\\\ax-risvis447\c$\calc';
print $DIR;  # prints "\\ax-risvis447\c$\calc"

# And if you want to use double quotes, escape the "$" too:
$DIR = "\\\\ax-risvis447\\c\$\\calc";
print $DIR;  # prints "\\ax-risvis447\c$\calc"