The function G(k) = /2 0 1 k2 sin2 t dt is called an elliptic integral of the second

Chapter 10, Problem 90

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The function G(k) = /2 0 1 k2 sin2 t dt is called an elliptic integral of the second kind. Prove that for |k| < 1, G(k) = 2 2 n=1 1 3 (2n 1) 2 4 (2n) 2 k2n 2n 1 9

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