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

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


    User Avatar
    Science Advisor

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook