I am reading some material which makes use of Landau(-Bachmann) notation for the asymptotic behavior of some error.
I started to wonder when this notation (especially the little $o$ on) has been first introduced and checked the Wikipedia source on this which states:
Earliest Uses of Symbols of Number Theory, 22. September 2006: (Memento vom 19. Oktober 2007 im Internet Archive) According to Wladyslaw Narkiewicz in The Development of Prime Number Theory:“The symbols O(·) and o(·) are usually called the Landau symbols. This name is only partially correct, since it seems that the first of them appeared first in the second volume of P. Bachmann’s treatise on number theory (Bachmann, 1894). In any case Landau (1909a, p. 883) states that he had seen it for the first time in Bachmann's book. The symbol o(·) appears first in Landau (1909a).”
I traced back the book and the page (where the reference is supposed to be found) using the quoted link, it's called
Handbuch der Lehre von der Verteilung der Primzahlen, Landau (p. 883)
but unfortunately, the book Handbuch der Lehre von der Verteilung der Primzahlen simply has not that many pages. It's a long shot, but: Does anyone know the precise page where I could find it?
I downloaded the Landau book and searched it.
The first occurrence of "big-oh" appears to be on page 31 with a discussion of Riemann's estimate of the number of zeros of the zeta function.
The first occurrences of "little-oh" appear to be on pages 69 and 70 in the form $\pi(x) = o(x)$. The definition is on page 70.
(Added after OP's comment - I somehow overlooked these)
The definition of big-oh is on page 59 and the definition of little-oh is on page 61.