A Crank Formula for π

I don't know why someone would make an AI slop fake of old mathematical crankery, but I think that has to be considered as a possibility. Especially given that the formula is being attributed to Dudley, who was actually cataloguing the nonsense of others.

(Also, a conventional Internet search tells me that Dudley was born in 1937, not 1912; and that rather than dying in 2005, he is still alive.)

(Perhaps Cook noticed these things and is too polite to point them out?)