Neglecting High-Order Terms in R: Tips & Tricks

[Juggler123]

Hi,

Is there a better way to write this?

'terms of order $O(R^{-Y})$ where $Y>1$ are neglected'

I feel like this is a bit clumsy.

Thanks for the help!

 

[Simon Bridge]

Other examples of order notation:
http://www.cse.buffalo.edu/~regan/cse250/order-notationhandout.pdf
http://en.wikipedia.org/wiki/Orders_of_approximation

For what you want - can Y be less than 0?
If not, then you are just accepting zero and 1st order terms in 1/R terms
... which is an O(1) approximation isn't it?

 

[Juggler123]

Yeah that's correct, if I am understanding little 'o' notation correctly I believe it's equivalent to write:

'terms of order $o(R^{-1})$ are neglected'

 

[Simon Bridge]

It is simpler to write it in terms of what orders you will accept.
Note, you wanted Y>1, so Y=1 (order -1) was accepted.

Take terms in (1/R) to 1st order.

 

[CellCoree]

I completely understand the importance of clear and concise language in scientific writing. In this case, I would suggest rephrasing the statement to something like: "Terms with orders greater than R^{-Y} (where Y>1) are disregarded." This removes the use of the word "neglected" and instead focuses on the specific terms that are being disregarded. Another option could be: "Terms with orders higher than R^{-Y} (where Y>1) are omitted." Overall, the key is to clearly convey the idea that certain terms are not being included in the analysis due to their high order. I hope this helps!