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
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.