Each call to dbConnect() will open a new connection to the database. One way of connecting only once is to declare the $dbh var as global to your package, and call dbConnect only once: 
my $dbh = dbConnect();

sub dbConnect {
  my $dsn = "DBI:mysql:database:localhost";
  my $db_user_name = 'username';
  my $db_password = 'password';

  $dbh = DBI->connect
    ($dsn, $db_user_name, $db_password, {RaiseError => 1}) || 
         die("cannot connect to DB: ".DBI::errstr."\n",$dbh);
  
}

sub foo {
    # Can still see $dbh in here
    my $sth = $dbh->prepare(...);
}

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Of course, this means you're connecting to the DB every time the script's called (which might not be necessary), and you won't be able to access $dbh from outside of this package (probably a good thing though, I prefer to confine all DB related stuff to one package, or at least one hierarchy of classes. The next step after this is Class::DBI).

In reply to Re: DBI / Mysql connections by Mutant
in thread DBI / Mysql connections by cyril

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