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%I #30 Jul 27 2023 12:18:41
%S 9,2,0,3,7,1,3,7,3,3,1,7,9,4,2,4,9,7,6,5,5,5,1,8,5,6,4,5,4,3,1,7,2,9,
%T 9,4,7,2,6,2,4,5,7,9,1,9,4,9,8,9,4,3,3,8,3,4,3,3,0,0,1,9,9,7,7,3,1,0,
%U 1,8,0,8,0,8,0,5,6,8,5,6,3,9,3,6,3,3,8,5
%N Decimal expansion of 1/(2*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.
%H Markus Faulhuber, Anupam Gumber, and Irina Shafkulovska, <a href="https://arxiv.org/abs/2209.04202">The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators</a>, arXiv:2209.04202 [math.CA], 2022, p. 2.
%F Equals 1/(2*A081760) = A175379/(2*A073005*A203145).
%F Equals Sum_{k,m in Z^2} exp(-Pi*(2/sqrt(3))*(k^2+k*m+m^2))*exp(2*Pi*i*(k/3-m/3)).
%F Equals Sum_{k>=0} (binomial(-1/3,2*k)^2 - binomial(-1/3,2*k+1)^2). - _Gerry Martens_, Jul 24 2023
%F Equals 3*Gamma(1/3)^3 / (2^(8/3) * Pi^2). - _Vaclav Kotesovec_, Jul 27 2023
%e 0.9203713733179424976555185645431729947262...
%t First[RealDigits[N[Gamma[1/6]/(2Gamma[1/3]Gamma[5/6]),88]]]
%o (PARI) 1/(2*gamma(1/3)*gamma(5/6)/gamma(1/6)) \\ _Michel Marcus_, Sep 24 2022
%Y Cf. A004117.
%Y Cf. A081760.
%Y Cf. A073005, A175379, A203145.
%K nonn,cons
%O 0,1
%A _Stefano Spezia_, Sep 23 2022
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