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Euler's Addition Theorem

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Let g(x)=(1-x^2)(1-k^2x^2). Then

int_0^a(dx)/(sqrt(g(x)))+int_0^b(dx)/(sqrt(g(x)))=int_0^c(dx)/(sqrt(g(x))),

where

c=(bsqrt(g(a))+asqrt(g(b)))/(sqrt(1-k^2a^2b^2)).

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Cite this as:

Weisstein, Eric W. "Euler's Addition Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulersAdditionTheorem.html

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