A196535 Decimal expansion of sum_{j=0..infinity} exp(-Pi*(2j+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

0,2

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.

Links

Table of n, a(n) for n=0..105.

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

Cf. A093580, A068466, A010767.

Sequence in context: A369110 A369826 A093580 * A106655 A105313 A085064

Adjacent sequences: A196532 A196533 A196534 * A196536 A196537 A196538

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