Formally describes something done according to an established custom, like dressing formally for dinner with the President, as people always have done.

In our casual era of wearing jeans almost everywhere and calling our elders by their first name, it's not every day that you meet someone who acts, speaks, or dresses more formally. But there is still value in this kind of expression, especially in showing respect on important occasions like weddings and funerals. Another meaning of the adverb formally is "officially," like being formally invited to dinner at the White House.

Definitions of formally

adv in a formal manner

“he was dressed rather formally
without formality

adv with official authorization

“the club will be formally recognized”

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