Question

power series of \(\sqrt{\dfrac{1-x}{1+x}}\)

Answer 1

Is there something I don't understand? Isn't power series just a Taylor series expansion? I don't think you need to ask this question with your mastery of math...

Answer 2

Something to do with spacetime diagrams?

Answer 3

not really, its just an approximation of doppler shift of light haha

\[f = f_0\sqrt{\dfrac{1-\beta}{1+\beta}} = f_0(1-\beta+\frac{1}{2}\beta^2)\]

assuming \(\beta \ll 1\)