Big-O notation, multiple variables

I'm looking for pointers to any discussion in the literature regarding the pitfalls involved in extending Big-O notation to multiple variables. It's been hard enough just to find a formal definition, as most authors define it only for 1 variable, even if they want to use it for multiple variables. However, the problems involved in extending the notation to multiple variables are severe enough that it would seem that the issue would have been treated somewhere in the literature. I'd also be interested in seeing any treatments comparing alternative definitions.

Thanks in advance,

Rod Howell
Associate Professor
Dept. of Computing and Information Sciences
Kansas State University
http://people.cis.ksu.edu/~rhowell/
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