{
  "coefficients": [
    "1/2",
    "11/2",
    "1/2"
  ],
  "pure_derivative_exponents": [
    {
      "k": 0,
      "rate": "7/2"
    },
    {
      "k": 1,
      "rate": "6/2"
    },
    {
      "k": 2,
      "rate": "5/2"
    },
    {
      "k": 3,
      "rate": "4/2"
    },
    {
      "k": 4,
      "rate": "3/2"
    },
    {
      "k": 5,
      "rate": "2/2"
    },
    {
      "k": 6,
      "rate": "1/2"
    },
    {
      "k": 7,
      "rate": "0/2"
    },
    {
      "k": 8,
      "rate": "-1/2"
    },
    {
      "k": 9,
      "rate": "-2/2"
    },
    {
      "k": 10,
      "rate": "-3/2"
    },
    {
      "k": 11,
      "rate": "-4/2"
    },
    {
      "k": 12,
      "rate": "-5/2"
    },
    {
      "k": 13,
      "rate": "-6/2"
    },
    {
      "k": 14,
      "rate": "-7/2"
    }
  ],
  "data": "eta0(x,y)=xy exp(-x^2-y^2) on the original positive quadrant",
  "exact_squared_norm_formula": "pi/128 sum (2i+1)!! (2j+1)!! exp((7-i-11j)t)",
  "scope": "Finite sums of exact proved norm formulas, evaluated numerically for the illustration; no numerical source profile or full stability certificate.",
  "samples": [
    {
      "t": 0.0,
      "homogeneous8_ratio": 1.0,
      "inhomogeneous8_ratio": 1.0
    },
    {
      "t": 0.1507537688442211,
      "homogeneous8_ratio": 0.5918002980150923,
      "inhomogeneous8_ratio": 0.5943547437597367
    },
    {
      "t": 0.3015075376884422,
      "homogeneous8_ratio": 0.5399127179516031,
      "inhomogeneous8_ratio": 0.5454932955295606
    },
    {
      "t": 0.4522613065326633,
      "homogeneous8_ratio": 0.49900233509328823,
      "inhomogeneous8_ratio": 0.5078310421088591
    },
    {
      "t": 0.6030150753768844,
      "homogeneous8_ratio": 0.4624254611591852,
      "inhomogeneous8_ratio": 0.4747020229677393
    },
    {
      "t": 0.7537688442211055,
      "homogeneous8_ratio": 0.4287796516332873,
      "inhomogeneous8_ratio": 0.4447481857769783
    },
    {
      "t": 0.9045226130653266,
      "homogeneous8_ratio": 0.39763308187121404,
      "inhomogeneous8_ratio": 0.41761778878162253
    },
    {
      "t": 1.0552763819095476,
      "homogeneous8_ratio": 0.3687595065241407,
      "inhomogeneous8_ratio": 0.39320677552412014
    },
    {
      "t": 1.2060301507537687,
      "homogeneous8_ratio": 0.3419847033071817,
      "inhomogeneous8_ratio": 0.371534457217811
    },
    {
      "t": 1.3567839195979898,
      "homogeneous8_ratio": 0.31715440175842957,
      "inhomogeneous8_ratio": 0.3527816254099883
    },
    {
      "t": 1.507537688442211,
      "homogeneous8_ratio": 0.2941270317103384,
      "inhomogeneous8_ratio": 0.3374494980844372
    },
    {
      "t": 1.658291457286432,
      "homogeneous8_ratio": 0.2727716097591264,
      "inhomogeneous8_ratio": 0.3267596420983345
    },
    {
      "t": 1.809045226130653,
      "homogeneous8_ratio": 0.2529667259307205,
      "inhomogeneous8_ratio": 0.32361498793444277
    },
    {
      "t": 1.9597989949748742,
      "homogeneous8_ratio": 0.23459979834276798,
      "inhomogeneous8_ratio": 0.33472305008950953
    },
    {
      "t": 2.1105527638190953,
      "homogeneous8_ratio": 0.2175664219115242,
      "inhomogeneous8_ratio": 0.37437537631461065
    },
    {
      "t": 2.2613065326633164,
      "homogeneous8_ratio": 0.20176977254696163,
      "inhomogeneous8_ratio": 0.468721142145528
    },
    {
      "t": 2.4120603015075375,
      "homogeneous8_ratio": 0.1871200562911029,
      "inhomogeneous8_ratio": 0.658481468353181
    },
    {
      "t": 2.5628140703517586,
      "homogeneous8_ratio": 0.17353399879815515,
      "inhomogeneous8_ratio": 1.0045381721027562
    },
    {
      "t": 2.7135678391959797,
      "homogeneous8_ratio": 0.16093437195253693,
      "inhomogeneous8_ratio": 1.604627718768194
    },
    {
      "t": 2.8643216080402008,
      "homogeneous8_ratio": 0.1492495548719132,
      "inhomogeneous8_ratio": 2.6234877895882005
    }
  ]
}