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%I #29 Aug 02 2023 13:49:42
%S 1,1,5,9,5,9,5,2,6,6,9,6,3,9,2,8,3,6,5,7,6,9,9,9,2,0,5,1,5,7,0,0,2,0,
%T 8,8,1,9,4,5,1,6,5,2,6,3,4,3,9,7,8,2,8,5,5,2,6,3,1,0,5,0,5,9,7,4,7,9,
%U 7,3,7,5,7,2,0,5,2,8,6,2,5,8,6,5,8,0,8,5,2,5
%N Decimal expansion of 2^(-2/3)/L, where L is the conjectured Landau's constant A081760.
%H Markus Faulhuber, <a href="https://doi.org/10.1007/s11139-019-00224-2">An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a "Weltkonstante"-or-how Ramanujan split temperatures</a>, The Ramanujan Journal volume 54, pages 1-27 (2021). See p. 23.
%F Equals A002580*A357318.
%F Equals A235362/A081760 = A235362*A175379/(A073005*A203145).
%F Equals Sum_{k,m in Z^2} exp(-Pi*(2/sqrt(3))*(k^2+k*m+m^2)).
%F From _Gerry Martens_, Jul 29 2023: (Start)
%F Equals hypergeom([1/3, 2/3], [1], 1/2).
%F Equals sqrt(Pi)/(Gamma(2/3)*Gamma(5/6)). (End)
%e 1.159595266963928365769992051570020881945...
%t First[RealDigits[N[2^(1/3)*Gamma[1/6]/(2Gamma[1/3]Gamma[5/6]), 90]]]
%Y Cf. A002580, A073005, A081760, A175379, A203145, A235362, A357318.
%K nonn,cons
%O 1,3
%A _Stefano Spezia_, Sep 23 2022
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