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A196535
Decimal expansion of sum_{j=0..infinity} exp(-Pi*(2j+1)^2).
0
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, 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, 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
OFFSET
0,2
REFERENCES
Jolley, Summation of Series, Dover (1961) eq (114) on page 22.
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 729, formula 14.
FORMULA
Equals (2^(1/4)-1) * Gamma(1/4) / ( 2^(11/4) * Pi^(3/4) ).
EXAMPLE
0.04321391826429779829201838202725...
MAPLE
(root[4](2)-1)*GAMMA(1/4)/2^(11/4)/Pi^(3/4) ; evalf(%) ;
MATHEMATICA
RealDigits[ EllipticTheta[2, 0, Exp[-4*Pi]]/2, 10, 105] // First // Prepend[#, 0]& (* Jean-François Alcover, Feb 12 2013 *)
CROSSREFS
KEYWORD
nonn,less,cons,easy
AUTHOR
R. J. Mathar, Oct 03 2011
EXTENSIONS
12 more digits from Jean-François Alcover, Feb 12 2013
STATUS
approved