Sunday, October 7, 2018

integration - Approximation for elliptic integral of second kind

My (physics) book gives the following approximation:



π/2π/21(1a2)sin(k)2dk2+(a1b1lna2)a2+O(a2lna2)



where a1 and b1 are "(unspecified) numerical constants." I've been looking for either a derivation of this, or the same approximation listed elsewhere and have gotten nowhere. Can someone help me along?

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