Expansion of Hydrogen GS (Relativistic)

[sean_mp]

Homework Statement

I'm trying to verify equations 16 and 17 on the attached paper, but I'm just not getting the same values they are. I've used mathematica and it just isn't happening. For one thing, there should be a factor of 1/2 in front of equation 16, but I'm really not seeing how they got this from a typical series expansion.

Homework Equations

I need help getting the same values as 16 and 17 in the paper. I'm just not getting it in my output.

The Attempt at a Solution

 

[fzero]

I don't have a lot to add, other than I plugged (14) into WolframAlpha and reproduced your factor of 1/2 (http://www.wolframalpha.com/input/?i=series+sqrt%281-+g%2F%28sqrt%28k^2%2Bg%29%2Bn-k%29^2%29+in+g+to+order+2). I have no idea why he gets something else.

 

[sean_mp]

Wow... I'm embarrassed that I didn't get this myself... I must have had a typo in my equation or something.

Thanks a lot, you're a lifesaver.