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I am writing something and met a notational conflicting. Is there any alternative notation for the remainder for a series, e.g. Taylor, expansion? It is typically denoted as R, but is there anything else and used before (I don't want to invent my own notation unless necessary)?

Any suggestion with reference is greatly appreciated!

Thank you very much in advance Ethan

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I've seen $\Delta f_N$ used to denote the remainder. For example, $$f(x) = \sum_{n=0}^{N} a_n x^n + \Delta f_N(x).$$ Whatever you choose, you can make a little note about what the symbol means to avoid confusing the reader. – Antonio Vargas Dec 17 '12 at 1:44
I've seen it denoted by $r_n(x)$, as well as directly by the integral estimate. – tomasz Dec 17 '12 at 2:17
Great!!!! I really appreciate your help. – Ethan Dec 17 '12 at 2:33
> Antonio Vargas Thank you so much for your suggestion! – Ethan Dec 17 '12 at 2:33

Take a look here and here, both of which use $R_N$ (or other subscript) to denote the remainder. In my experience, this is the most common.

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Thanks a lot. I know $R$ is the most common one, but there is a lot of $R$ denotes to something else in my essay. That's also common in other convention... – Ethan Dec 17 '12 at 2:33

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