. Vinogradov's two notations enjoy visual symmetry, asfor positive functions , we have

In 1976, Donald Knuthdefined

which has the same meaning as Vinogradov's .

However, much earlier, Hardy and Littlewood had defined differently, and their notation enjoys widespread use today in analytic number theory.Justifying his use of the -symbol to describe a stronger property, Knuth wrote: "For all the applications I have seen so far in computer science, a stronger requirement ...

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