What is a coefficient of order unity?

1. Nov 7, 2006

tony873004

Does anyone know what a coefficient of order unity is? I'm reading a journal paper and it gives the formula
$$P_{KOZ} \simeq P_1 \left( {\frac{{m_0 + m_1 }}{{m_2 }}} \right)\left( {\frac{{a_2 }}{{a_1 }}} \right)^3 \left( {1 - e_2^2 } \right)^{3/2}$$
and then it says
.

It's on page 6 of this paper : http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v535n1/40691/406 [Broken] 91.web.pdf

Last edited by a moderator: Apr 22, 2017 at 1:52 PM
2. Nov 7, 2006

Sane

I'm sorry I can't help. Perhaps me bumping this up can get other people to see it additionally. However! Wikipedia is your friend!

$$\zeta(z;\Lambda)=\frac{1}{z}-\sum_{k=1}^{\infty}\mathcal{G}_{2k+2}(\Lambda)z^{2k+1}$$

where $$\mathcal{G}_{2k+2}$$ is the Eisenstein series of weight $$2k+2$$.

So find the "coefficient of order unity" by using this function, then multiply it in to whatever expression you're dealing with.

3. Nov 7, 2006

StatusX

It means they are being sloppy and not calculating constants that go out front. These will be mathematical constants, like combinations of pi, e, etc, and will be not too small or too large, ie, probably in the range 1/10 to 10. So you might say what they have there is an approximation, although you should keep in mind that there is a constant that they could multiply it by that would make it exact for all values of whatever variable the function varies over, and this is something that isn't true in general of approximations.

4. Nov 8, 2006

DrGreg

It may mean O(1) in the sense defined "http://en.wikipedia.org/wiki/Big_oh" [Broken].

In short, the value remains finite as something else in the expression approaches some limit (e.g. infinity or zero depending on context).

Last edited by a moderator: Apr 22, 2017 at 1:54 PM
5. Nov 8, 2006

chroot

Staff Emeritus
It means a small, unspecified constant in the same order of magnitude as one.

- Warren

6. Nov 8, 2006

tony873004

I guess that would imply that the answer given by the formula would be within an order of magnitude of correct without the unspecified constant.