Wordnet 3.0
ADVERB (1)
1.
exerting influence;
The Collaborative International Dictionary of English v.0.48:
Influentially \In`flu*en"tial*ly\, adv.
In an influential manner.
[1913 Webster]
WordNet (r) 3.0 (2006):
influentially
adv 1: exerting influence