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Decimal expansion of 1/(1+1/(1+2/(1+3/(1+4/(1+5/(1+...)))))).
5

%I #20 Feb 03 2017 14:56:41

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

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

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

%N Decimal expansion of 1/(1+1/(1+2/(1+3/(1+4/(1+5/(1+...)))))).

%C Term of Ramanujan's formula (see A059444 and A060196).

%D S. R. Finch, "Mathematical Constants", Cambridge, pp. 423-428.

%H G. C. Greubel, <a href="/A108088/b108088.txt">Table of n, a(n) for n = 0..5000</a>

%F Equals sqrt(Pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function. - _Daniel Forgues_, Apr 14 2011

%F Also equals Integral_{-infinity..infinity} (1/sqrt(2*Pi))*exp(-x^2/2)/(1+x^2) dx, where the integrand is normal PDF times Cauchy PDF. - _Jean-François Alcover_, Apr 28 2015

%e 0.6556795424187984715438712307308112833992823328704...

%t RealDigits[Sqrt[Pi*E/2]*Erfc[1/Sqrt[2]], 10, 111][[1]]

%o (PARI) sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2)) \\ _G. C. Greubel_, Feb 03 2017

%Y Cf. A111129.

%K nonn,cons

%O 0,1

%A _Philippe Deléham_, Jun 21 2005