The Wikipedia page of this article is basically a masterclass why Wikipedia is useless for learning technical subjects. They are not even able to teach such a simple subject properly there!

Bibliography:

- www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf gives a definition that does not consider upper and lower indexes, it only counts how many times the indices appearTheir definition of the Laplacian is a bit wrong as only one $i$ appears in it, they likely meant to have written $∂x_{i}∂ ∂x_{i}∂F $ instead of $∂x_{i}∂_{2}F $, related: