1) As regards form 2) Authoritatively 3) How to dress for a ball 4) In a formal manner 5) In writing 6) Legitimately 7) Officially 8) On the record 9) Publicly 10) Strictly speaking 11) With authorization 12) With official authorization 1) Coolly 2) Officially 
• (adv.) In a formal manner; essentially; characteristically; expressly; regularly; ceremoniously; precisely.
Form'al·ly adverb In a formal manner; essentially; characteristically; expressly; regularly; ceremoniously; precisely. « That which formally makes this [ charity] a Christian grace, is the spring from which it flows.» Smalridge. « You and your followers do stand f...
[adv] - with official authorization 2. [adv] - in a formal manner
adverb in a formal manner; `he was dressed rather formally`
(in Scholasticism) Is sometimes trtken for mentally, i.e. according to the formalities which we distinguish by the mind alone. When formally is so understood, it has as its correlative really. Thus the omnipotence and the wisdom of God are not really but formally distinct. It is also said of the thing considered in itself or in its proper entity. ....
in a formal manner: The store was formally opened on Tuesday. · as regards form; in form: It may be formally correct, but it is substantively wrong.