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Decimal expansion of sum_{j=0..infinity} exp(-Pi*(2j+1)^2).
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%I #14 Jun 08 2020 10:24:39

%S 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 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 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 Decimal expansion of sum_{j=0..infinity} exp(-Pi*(2j+1)^2).

%D Jolley, Summation of Series, Dover (1961) eq (114) on page 22.

%D A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 729, formula 14.

%F Equals (2^(1/4)-1) * Gamma(1/4) / ( 2^(11/4) * Pi^(3/4) ).

%e 0.04321391826429779829201838202725...

%p (root[4](2)-1)*GAMMA(1/4)/2^(11/4)/Pi^(3/4) ; evalf(%) ;

%t RealDigits[ EllipticTheta[2, 0, Exp[-4*Pi]]/2, 10, 105] // First // Prepend[#, 0]& (* _Jean-François Alcover_, Feb 12 2013 *)

%Y Cf. A093580, A068466, A010767.

%K nonn,less,cons,easy

%O 0,2

%A _R. J. Mathar_, Oct 03 2011

%E 12 more digits from _Jean-François Alcover_, Feb 12 2013