
#1
Feb2712, 09:56 AM

P: 37

When I am reading the paper about Rayleigh instability, I found this type of expanding method.
[tex] \sqrt{1+(\frac{2\pi\delta}{\lambda})^2 \cos^2(\frac{2\pi x}{\lambda})} = 1 + \frac{1}{2}(\frac{2\pi\delta}{\lambda})^2\cos^2 (\frac{2\pi x}{\lambda}) + \cdots [/tex] Can someone tell me what type of expansion is this? 



#2
Feb2712, 10:18 AM

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P: 6,344

It's the Binomial series expansion of ##(1+x)^{1/2}##




#3
Feb2712, 10:27 AM

P: 37

[tex] \frac{d(1 + f(x))^{\frac{1}{2}}}{df(x)} = \frac{1}{2} \frac{1}{\sqrt{1 + f(x)}} [/tex] 



#4
Feb2712, 01:31 PM

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P: 6,344

What type of expansion is this?
I'm not sure where that is leading to. I meant
##(1+x)^n = 1 + n x + n(n1)x^2 / 2! + n(n1)(n2)x^3/3! + \dots## where x is the trig function and n = 1/2. 



#5
Feb2712, 07:30 PM

P: 37




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