A128892 - OEIS

%I #38 Jan 12 2017 04:43:03

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

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

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

%N Decimal expansion of 2*(1 + Pi*e^Pi*(1 + erf(sqrt(Pi)))).

%C The continued fraction is: 291, 44, 1, 6, 3, 17, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 3, 1, 4, 10, 13, 2, 3, 26, ..., . - _Robert G. Wilson v_, Jun 09 2007

%C Increasing partial quotients: 44, 66, 75, 239, 280, 563, 577, 938, 8243, 8674, 30243, 130392, 1564166, ..., at positions: 1, 74, 105, 190, 232, 382, 518, 1543, 1761, 2330, 12204, 34946, 41957, ... - _Robert G. Wilson v_, Jun 09 2007

%C The constant is equal to Sum_{n>=0} S_n, where S_n is the area of an n-dimensional sphere of unit radius. This constant and the constant of A128891 are connected by the equation Sum_{n>=0}S_n - 2*Pi*Sum{n>=0}V_n = 2, where V_n is the volume of an n-dimensional sphere of unit radius. - _Philippe A.J.G. Chevalier_, Dec 17 2015

%H G. C. Greubel, <a href="/A128892/b128892.txt">Table of n, a(n) for n = 3..5003</a>

%F 2*(1 + Pi*e^Pi*(1 + erf(sqrt(Pi)))).

%e 291.0222898249729824484089300040636921153978386238850492613995903...

%t RealDigits[ 2*(1 + Pi*E^Pi*(1 + Erf[Sqrt[Pi]])), 10, 111][[1]] (* _Robert G. Wilson v_, Jun 09 2007 *)

%o (MATLAB) 2*(1+pi*exp(pi)*(1+erf(sqrt(pi)))) \\ _Altug Alkan_, Nov 11 2015

%o (PARI) 2*(1+Pi*exp(Pi)*(2-erfc(sqrt(Pi)))) \\ _Michel Marcus_, Nov 11 2015

%Y Cf. A128891.

%K cons,nonn

%O 3,1

%A _Philippe Deléham_, Apr 20 2007

%E More terms from _Robert G. Wilson v_, Jun 09 2007