## Asymptotic Notation

Let be a integer variable which tends to infinity and let be a continuous variable tending to some limit. Also, let or be a positive function and or any function. Then Hardy and Wright (1979) define

1. to mean that for some constant and all values of and ,

2. to mean that ,

3. to mean that ,

4. to mean the same as ,

5. to mean , and

6. to mean for some positive constants and .
implies and is stronger than .

References

Hardy, G. H. and Wright, E. M. Some Notation.'' §1.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 7-8, 1979.