Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is a coefficient of order unity?

  1. Nov 7, 2006 #1

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    Does anyone know what a coefficient of order unity is? I'm reading a journal paper and it gives the formula
    [tex]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} [/tex]
    and then it says
    .

    It's on page 6 of this paper : http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v535n1/40691/406 91.web.pdf
     
  2. jcsd
  3. Nov 7, 2006 #2
    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.

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

    where [tex]\mathcal{G}_{2k+2}[/tex] is the Eisenstein series of weight [tex]2k+2[/tex].

    So find the "coefficient of order unity" by using this function, then multiply it in to whatever expression you're dealing with.
     
  4. Nov 7, 2006 #3

    StatusX

    User Avatar
    Homework Helper

    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.
     
  5. Nov 8, 2006 #4

    DrGreg

    User Avatar
    Science Advisor
    Gold Member

    It may mean O(1) in the sense defined here.

    In short, the value remains finite as something else in the expression approaches some limit (e.g. infinity or zero depending on context).
     
  6. Nov 8, 2006 #5

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    - Warren
     
  7. Nov 8, 2006 #6

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    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 definately learned a lot from this thread and the semi-related "What's the difference...?" thread.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is a coefficient of order unity?
  1. What is Unity? (Replies: 3)

Loading...