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Decimal expansion of the arithmetic-geometric mean (AGM) of Pi and e.
3

%I #27 Jul 05 2023 06:08:08

%S 2,9,2,6,1,0,8,5,5,1,5,7,2,3,0,4,6,9,6,6,6,5,8,9,5,7,1,0,1,7,0,5,5,8,

%T 5,3,1,0,6,6,2,0,5,7,5,5,3,7,9,8,4,5,6,2,7,4,4,2,4,1,5,5,1,2,4,2,1,5,

%U 2,6,8,6,8,5,1,1,9,8,6,4,4,5,1,9,3,9,4,0,9,3,5,4,6,3,2,2,7,4,5,6,4,1,8,3,1

%N Decimal expansion of the arithmetic-geometric mean (AGM) of Pi and e.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Arithmetic-GeometricMean.html">Arithmetic-Geometric Mean</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean">Arithmetic-geometric mean</a>

%e AGM(Pi,e) = 2.926108551572304696665895710170558531...

%p evalf(GaussAGM(Pi, exp(1)), 144); # _Alois P. Heinz_, Jul 05 2023

%t RealDigits[ArithmeticGeometricMean[Pi, E], 10, 100][[1]] (* _Amiram Eldar_, May 31 2021 *)

%o (PARI) agm(exp(1),Pi) \\ _Charles R Greathouse IV_, Mar 03 2016

%Y Cf. A000796, A001113.

%K nonn,cons

%O 1,1

%A _Zak Seidov_, Oct 05 2002