A355178 Decimal expansion of 2^(-2/3)/L, where L is the conjectured Landau's constant A081760.

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, 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, 7, 3, 7, 5, 7, 2, 0, 5, 2, 8, 6, 2, 5, 8, 6, 5, 8, 0, 8, 5, 2, 5

Offset: 1

Author

Stefano Spezia, Sep 23 2022

Keywords

• nonn
• cons

Examples

			1.159595266963928365769992051570020881945...
		

Links

• Markus Faulhuber, An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a "Weltkonstante"-or-how Ramanujan split temperatures, The Ramanujan Journal volume 54, pages 1-27 (2021). See p. 23.

Crossrefs

Cf. A002580, A073005, A081760, A175379, A203145, A235362, A357318.

Programs

Mathematica

First[RealDigits[N[2^(1/3)*Gamma[1/6]/(2Gamma[1/3]Gamma[5/6]), 90]]]

Formula

Equals A002580*A357318.

Equals A235362/A081760 = A235362*A175379/(A073005*A203145).

Equals Sum_{k,m in Z^2} exp(-Pi*(2/sqrt(3))*(k^2+k*m+m^2)).

From Gerry Martens, Jul 29 2023: (Start)

Equals hypergeom([1/3, 2/3], [1], 1/2).

Equals sqrt(Pi)/(Gamma(2/3)*Gamma(5/6)). (End)