A172084 Decimal expansion of the constant x that satisfies Arithmetic-Geometric-Mean(3,x) = Pi.

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

Offset: 1

Author

Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Jan 25 2010

Keywords

• cons
• nonn

Examples

			AGM(3,3.28645055277941042287...) = Pi = A000796.
		

Links

• Gerd Lamprecht, Iterationsrechner mit Algorithmus.
• Gerd Lamprecht, Zahlenfolgen (sequences).
• Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean.

Crossrefs

Cf. A000796, A053004.

Programs

Mathematica

RealDigits[x /. FindRoot[ArithmeticGeometricMean[3, x] == Pi, {x, 4}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, May 25 2023 *)

PARI

solve(x=3,4,agm(3,x)-Pi) \\ Charles R Greathouse IV, Mar 03 2016