A357318 Decimal expansion of 1/(2*L), where L is the conjectured Landau's constant A081760.

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, 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, 1, 8, 0, 8, 0, 8, 0, 5, 6, 8, 5, 6, 3, 9, 3, 6, 3, 3, 8, 5

Offset

0,1

Links

Table of n, a(n) for n=0..87.

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.

Markus Faulhuber, Anupam Gumber, and Irina Shafkulovska, The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators, arXiv:2209.04202 [math.CA], 2022, p. 2.

Formula

Equals 1/(2*A081760) = A175379/(2*A073005*A203145).

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)).

Equals Sum_{k>=0} (binomial(-1/3,2*k)^2 - binomial(-1/3,2*k+1)^2). - Gerry Martens, Jul 24 2023

Equals 3*Gamma(1/3)^3 / (2^(8/3) * Pi^2). - Vaclav Kotesovec, Jul 27 2023

Example

0.9203713733179424976555185645431729947262...

Mathematica

First[RealDigits[N[Gamma[1/6]/(2Gamma[1/3]Gamma[5/6]), 88]]]

Prog

(PARI) 1/(2*gamma(1/3)*gamma(5/6)/gamma(1/6)) \\ Michel Marcus, Sep 24 2022

Crossrefs

Cf. A004117.

Cf. A081760.

Cf. A073005, A175379, A203145.

Sequence in context: A335539 A193373 A246564 * A327995 A019876 A155696

Adjacent sequences: A357315 A357316 A357317 * A357319 A357320 A357321

Keyword

nonn,cons

Author

Stefano Spezia, Sep 23 2022

Status

approved