mysql_real_escape_string(): Access denied for user ''@'localhost' (using passwor

I’ve started receiving this error (in the topic title) in a plugin after migrating my website to a different hosting package.

It appears this line of code is causing the error:
.mysql_real_escape_string($recipients[$i]).

I’ve got no idea what this means or does. I’ve repaired/optimized the database, I’ve re-installed an older version of WordPress, I’ve deactivated all plugins and changed theme however none of these changed anything.

Any ideas anyone?