A113014 - OEIS

%I #16 Aug 22 2023 20:42:56

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

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

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

%N Decimal expansion of value of the continued fraction 1/(2+3/(4+5/(6+7/....

%C This fraction equals sqrt(2e/Pi)/erfi(1/sqrt(2)) - 1. - _Robert Israel_, Aug 29 2007

%H G. C. Greubel, <a href="/A113014/b113014.txt">Table of n, a(n) for n = 0..10000</a>

%H Sci.math, <a href="http://groups.google.com/group/sci.math/browse_thread/thread/9a56745424d4262f/6ea7ddfb3f7e1d8c?lnk=gst&amp;q=bhushit#6ea7ddfb3f7e1d8c">Continued Fractions</a>.

%e 0.3797319547409956328...

%t n=150; s=n; While[n-2>=0, s=n-2 + (n-1)/s; n=n-2]; RealDigits[N[s, 120]][[1]]

%t RealDigits[N[Sqrt[2E/Pi]/Erfi[1/Sqrt[2]]-1,120]][[1]] (* _T. D. Noe_, Oct 06 2008 *)

%o (PARI) {Erfi(z) = -I*(1.0-erfc(I*z))};

%o real(sqrt(2*exp(1)/Pi)/Erfi(1/sqrt(2)) - 1) \\ _G. C. Greubel_, Apr 09 2018

%Y Cf. A365105, A365116.

%K cons,nonn

%O 0,1

%A _T. D. Noe_, Oct 10 2005

%E Sci.math link from Bhushit Joshipura (joshipura(AT)gmail.com), Jul 15 2008