Help with expansion of an expression

AI Thread Summary
The discussion centers on understanding the expansion of the expression 1/sqrt{1+[2(r-r')*d]/(r-r')^2} using Taylor series. The author seeks clarification on how to derive the approximation 1 - {[(r-r')*d]/(r-r')^2 + ...}. It is suggested that the expansion involves applying Taylor series to the function 1/sqrt(1+x), which approximates to 1 - x/2 for small values of x. Participants discuss the steps needed to achieve this approximation and confirm that the approach is indeed a Taylor expansion. The conversation emphasizes the importance of understanding the underlying mathematics in vector contexts.
sliorbra
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Hello,

I have a problem to understand how the author made the following expansion:


1/sqrt{1+[2(r-r')*d]/(r-r')^2}≈1-{[(r-r')*d]/(r-r')^2+...}

where all the letters go for vectors and the symbol '*' is the dot product.
I suppose it is a Taylor expansion, but i just don't get it in this case.


Can someone give me the way?
 
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1/sqrt(1+x) ≈ 1/(1+x/2) ≈ 1-x/2
Two taylor expansions up to the linear term.
 
thank you!
 
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