Caroline Greatorex, 55, was struck by the Honda Accord cab on Friarwood Lane, at the junction with Southgate, at around 6.45am on December 1.
She was taken to Leeds General Infirmary but died three weeks later on December 21.
An inquest into Ms Greatorex’s death was opened by area coroner Jonathan Leach at Wakefield Coroner’s Court on Monday.
Mr Leach said that a postmortem was carried out and her cause of death was recorded as bronchopneumonia, caused by the head injuries she suffered in the collision.
Mr Leach adjourned the inquest with a date to be fixed at a later date.
The devastated family of Ms Greatorex, who lived on Bondgate in Pontefract, released a photo of her recently as they appealed for anyone who may have witnessed the collision.
A 38-year-old man arrested on suspicion of causing serious injury by dangerous driving was later released under investigation.
Detective Sergeant Fiona Hoodless from the Major Collision and Enquiry Team, said: “I am particularly keen to speak to anyone who saw the collision, or who saw the involved vehicle before the collision, or anyone with dashcam or mobile phone footage.”
Anyone with details is being asked to contact police on 101 and quote log 362 from December 1.