This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A196535 #26 Jul 03 2025 09:18:16
%S A196535 0,4,3,2,1,3,9,1,8,2,6,4,2,9,7,7,9,8,2,9,2,0,1,8,3,8,2,0,2,7,2,5,0,3,
%T A196535 4,1,8,4,2,0,6,0,4,4,7,7,1,2,9,3,7,4,6,3,1,2,5,2,7,3,4,4,6,1,7,8,9,8,
%U A196535 7,1,8,0,7,2,3,7,7,5,1,7,0,4,9,9,3,1,8,1,5,8,7,8,2,5,2,4,9,0,6,2,8,4,7,1,6,0
%N A196535 Decimal expansion of Sum_{j=0..oo} exp(-Pi*(2*j+1)^2).
%D A196535 Jolley, Summation of Series, Dover (1961) eq (114) on page 22.
%D A196535 A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 729, formula 14.
%H A196535 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007), p. 78.
%F A196535 Equals (2^(1/4)-1) * Gamma(1/4) / ( 2^(11/4) * Pi^(3/4) ).
%F A196535 Equals theta2(exp(-4*Pi))/2.
%e A196535 0.04321391826429779829201838202725...
%p A196535 (root[4](2)-1)*GAMMA(1/4)/2^(11/4)/Pi^(3/4) ; evalf(%) ;
%t A196535 RealDigits[ EllipticTheta[2, 0, Exp[-4*Pi]]/2, 10, 105] // First // Prepend[#, 0]& (* _Jean-François Alcover_, Feb 12 2013 *)
%Y A196535 Cf. A093580, A068466, A010767.
%K A196535 nonn,less,cons,easy
%O A196535 0,2
%A A196535 _R. J. Mathar_, Oct 03 2011
%E A196535 12 more digits from _Jean-François Alcover_, Feb 12 2013