Definition of "hoping"

These things write I unto thee, hoping to come unto thee shortly:

1611, The Holy Bible, […] (King James Version), London: […] Robert Barker, […], 1 Timothy 3:13

The miserable man cast a wistful look towards the east, hoping to see the first faint streaks of day.

1841 February–November, Charles Dickens, “Barnaby Rudge”, in Master Humphrey’s Clock, volume III, London: Chapman & Hall, […], chapter 18