What is a coefficient of order unity?

[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

This expression should be multiplied by a coefficient of order unity that can be obtained using Weierstrass's zeta function

.

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

 

[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!

This article seems to briefly explain the Weierstrass's zeta function.

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

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 into whatever expression you're dealing with.

 

[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.

 

[DrGreg]

Does anyone know what a coefficient of order unity is?

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

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

 

[chroot]

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

- Warren

 

[tony873004]

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

- Warren

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.

Thanks everyone for your answers. I definitely learned a lot from this thread and the semi-related "What's the difference...?" thread.