A096428 - OEIS

%I #14 Feb 16 2025 08:32:53

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

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

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

%N Decimal expansion of (4*sqrt(2)*Pi^2)/gamma(1/4)^2.

%C Asymptotic constant in the expected perimeter of square point picking.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric Probability Constants, p. 481.

%H G. C. Greubel, <a href="/A096428/b096428.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePointPicking.html">Square Point Picking</a>

%e 4.247296545963878651221513149595788524022238578931556848162...

%t RealDigits[(4*Sqrt[2]*Pi^2)/Gamma[1/4]^2, 10, 100][[1]] (* _G. C. Greubel_, Sep 27 2018 *)

%o (PARI) (4*sqrt(2)*Pi^2)/gamma(1/4)^2 \\ _Michel Marcus_, Jun 26 2014

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 4*Sqrt(2)*Pi(R)^2/Gamma(1/4)^2; // _G. C. Greubel_, Sep 27 2018

%Y Cf. A097060.

%K nonn,cons,changed

%O 1,1

%A _Eric W. Weisstein_, Jul 21 2004