A.T. Robertson Commentary Luke 7:4

"And they, when they came to Jesus, besought him earnestly, saying, He is worthy that thou shouldest do this for him;" — Luke 7:4 (ASV)

Besought (παρεκαλουν). Imperfect active, began and kept on beseeching. This is the same verb used by Matthew in Mt 8:5 of the centurion himself.

Earnestly (σπουδαιως). From σπουδη haste. So eagerly, earnestly, zealously, for time was short.

That thou shouldst do this for him (ω παρεξη τουτο). Second future middle singular of παρεχω. Old and common verb, furnish on thy part. Hω is relative in dative case almost with notion of contemplated result (Robertson, Grammar, p. 961).