A Basic Introduction of Bachmann-Landau AsymptoticNotation
Paul Bachmann introduced the $O$ notation in his book Die Analytische Zahlentheorie
while working on asymptotic estimates and handling error terms in analytic number theory.
His ideas served as inspiration for Edmund Landau, who further refined the concept and introduced a stronger variant
known as the little $o$ notation in his book Handbuch der Lehre von der Verteilung der Primzahlen. These notations are now
extensively used in the field of analytic number theory.
Although mathematicians generally grasp the meaning of big $O$ and little $o$ notation intuitively, effectively
communicating their precise definitions can sometimes pose challenges. Therefore, this paper aims to thoroughly comprehend the essence of big $O$ and
little $o$ notation and elucidate how to appropriately apply them in various mathematical contexts.
About
This paper aims to thoroughly elucidate how to appropriately apply big-O and little-o notation in various mathematical contexts.