reference-values.json

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{
  "T283": {
    "title": "Mahler measures of $1+x_1+\\dots+x_{n-1}$ (uniform random walks in the plane)",
    "values": {
      "3": {
        "comment": "Smyth's value $\\mu_3=\\mathrm{Cl}_2(\\pi/3)/\\pi=\\frac{3\\sqrt3}{4\\pi}L(2,\\chi_{-3})$.",
        "number": "0.32306594721945051409363651072380639407224184078059"
      },
      "4": {
        "comment": "Smyth's value $\\mu_4=7\\zeta(3)/(2\\pi^2)$.",
        "number": "0.42627839881750579092352142659616687305800676962964"
      }
    }
  },
  "T393": {
    "title": "Watson integrals of the cubic lattices",
    "values": {
      "number": "1.344661183165144296349156350052455748708176605124362191475225098059839519670920404713506548841411718",
      "comment": "The lattice is face-centred cubic."
    }
  },
  "T296": {
    "title": "Complete elliptic integral of the first kind $K(m_r)$ at the singular values",
    "values": {
      "number": "1.598142002112540144460965105390112888900611097136742843395001850717051182376299048153673076745023371",
      "comment": "$K(m_3)=3^{1/4}\\Gamma(1/3)^3/(2^{7/3}\\pi)$ CITE{MathWorldSingularValue}."
    }
  }
}