We know that some charms need exact hand movement like Wingardium Leviosa. Is there such specific wand movement for Patronus Charm too? I have visited the Harry Potter Wikia of Patronus Charm. It says there is a specific wand movement. Below is the image.
This hand movement is used by Luna Lovegood and some others while practicing the charm when they were part of Dumbledore's Army. Also in the movie Harry Potter and the Deathly Hallows part 2, Severus Snape uses this specific hand movement to show his Doe Patronus to Dumbledore.
But while conjuring his first corporeal Patronus, Harry just points his wand into air and shouts Expecto Patronum. The spell works and his stag Patronus fends off 100+ dementors.
So, Is there any specific wand movement for Expecto Patronum?