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# Gauss's constant

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Or Gauss’ constant or Gauss constant (please put all these in the synonyms box). Designated $G$ in relation to the gamma function.

Approximately 0.8346268416740731862…

Listed in A014549 of Sloane’s OEIS. A comment reads: ”On May 30, 1799, Gauss discovered that this number is also equal to (2/Pi)*Integral(1/sqrt(1-t^4),t=0..1).”

Weisstein defines as ”The reciprocal of the arithmetic-geometric mean of $1$ and $\sqrt{2}$.”

MSC codes for ArithmeticGeometricMean are 26E60 (Real functions :: Miscellaneous topics :: Means) and 33E05 (Special functions :: Other special functions :: Elliptic functions and integrals), so I’d guess this apply here as well.

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