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A111129 Decimal expansion of the continued fraction 1+1/(1+2/(1+3/(1+4/(1+5/(1+...))))). 9


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

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

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

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

%D B. C. Berndt, Y.-S. Choi and S.-Y. Kang, The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society, Continued Fractions: From Analytic Number Theory to Constructive Approximation, ed. B. C. Berndt and F. Gesztesy, Amer. Math. Soc., 1999, pp. 15-56.

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

%D H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, 1948, pp. 356-358, 367

%H G. C. Greubel, <a href="/A111129/b111129.txt">Table of n, a(n) for n = 1..5000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFractionConstants.html">Continued Fraction Constants</a>

%H Eric Weissteinn's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedContinuedFractionConstant.html">Generalized Continued Fraction</a>

%F Equals the reciprocal of sqrt(pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function.

%e 1.52513527616098120908909053639057871330711636492060333554631394242...

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

%o (PARI) 1/(sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2))) \\ _G. C. Greubel_, Jan 24 2017

%Y Cf. A099287, A108088, A111188.

%Y Cf. A225435, A225436 (numerators and denominators of convergents to c.f.).

%K nonn,cons

%O 1,2

%A _N. J. A. Sloane_, based on correspondence from Tom Raes (tommy1729(AT)hotmail.com) and _Steven Finch_, Sep 22 2005

%E More terms from _Robert G. Wilson v_ and _Hans Havermann_, Oct 17 2005

%E Definition corrected by _Steven Finch_, Feb 05 2009

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Last modified August 7 09:16 EDT 2020. Contains 336274 sequences. (Running on oeis4.)