More Math Help with Albert

1. Apr 26, 2004

OneEye

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. Apr 26, 2004

HallsofIvy

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.

3. Apr 26, 2004

OneEye

HoI - Thanks - I suspected something like this, but lacked the mathematical toolkit to know what exactly was meant.