A196535 Decimal expansion of Sum_{j=0..oo} exp(-Pi*(2*j+1)^2).

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

Author

R. J. Mathar, Oct 03 2011

Keywords

• nonn
• less
• cons
• easy

Examples

			0.04321391826429779829201838202725...
		

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.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007), p. 78.

Crossrefs

Cf. A093580, A068466, A010767.

Programs

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 *)

Formula

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

Equals theta2(exp(-4*Pi))/2.

Extensions

12 more digits from Jean-François Alcover, Feb 12 2013