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In page Catalan's constant:

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If E(k) is the complete elliptic integral of the second kind, as a function of the elliptic modulus k, then[citation needed] G = − 1 2 + ∫ 0 1 E ( k ) d k . {\displaystyle G=-{\frac {1}{2}}+\int _{0}^{1}\mathrm {E} (k)\,dk.}