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Some kind of mathematical formula that I obviously dont know about?

  1. Nov 29, 2011 #1
    Hello there.
    Can you please explain the following:
    Let us suppose that δ is very much less than r, and expand |r+δ|^-1 in powers of δ/r. Keeping the lower order terms gives:
    |r+δ|^-1 ≈ 1/r.(1-r.δ/r^2) + 1/2r [3(δ.r/r)^2-(δ/r)^2]

    How did they reach here? is this kind of a mathematical formula that i dont know about?

    Thanks in advance
     
  2. jcsd
  3. Nov 29, 2011 #2
    I don't know that your aproximation is correct? If I set δ = 0 then the equation becomes

    1/|r| ≈ 1/r

    That doesn't look right?
     
  4. Nov 29, 2011 #3

    mathman

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    |r+δ| = |r||1+δ/r|. Since δ/r << 1, you may use |r|(1+δ/r).

    Take the reciprocal and expand (1+δ/r)-1 in a power series.
     
  5. Nov 29, 2011 #4
    What do you exactly mean by a power series, mathman?
     
  6. Nov 30, 2011 #5

    NascentOxygen

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    See the binomial series, and use just the first few terms, since they diminish rapidly for d/r very much smaller than 1: http://mathworld.wolfram.com/BinomialSeries.html
     
  7. Nov 30, 2011 #6

    NascentOxygen

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    I would check the approximation formula that you quote, too. That is, evaluate it for a small delta/r, say, .0015, and verify that it gives a good approximation. (Otherwise you might be futilely trying to arrive at a formula that you have transcribed wrongly. I haven't checked it.)
     
  8. Nov 30, 2011 #7
    Thank you, NascentOxygen. I get it now. :)
     
  9. Nov 30, 2011 #8

    mathman

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    (1+x)-1 = 1 - x + x2 - x3 + x4 - ....

    Formula holds for |x| < 1.
     
  10. Dec 1, 2011 #9
    Thank you.
     
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