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More Math Help with Albert

  1. Apr 26, 2004 #1
    In Relativity, (p. 45), Dr. Einstein says:

    How does one get from the second equation to the third? What is meant by "develop[ing] the expression... in the form of a series"?

    Any help would be more than appreciated.
  2. jcsd
  3. Apr 26, 2004 #2


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    One way is to use a "Taylor's series" expansion.

    If f is any function, analytic at x0 then
    f(x)= f(x0)+ f '(x0)(x- x0)+ (f''(x0)/2)(x- x0)2+ (f'''(x0)/6)(x- x0)3+ ...
    the general term is (f(n)(x0)/n!)(x-x0)n where f(n) is the nth derivative.

    In particular, use the "McLaurin series" which is the Taylor's series with x0= 0 and f(x)= (1+ x2/c2)-1/2, set x= v, and then multiply by mc2.
  4. Apr 26, 2004 #3
    HoI - Thanks - I suspected something like this, but lacked the mathematical toolkit to know what exactly was meant.

    Most helpful!
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