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Gauss quadrature rules for evaluating integrals of the form  \[    2 π  −  1 / 2 −  ∫  0 ∞  exp ⁡  ( −  x 2 ) f ( x ) d x 2{\pi ^{ - 1/2}} - \smallint _0^\infty \exp ( - {x^2})f(x)dx     \]  have been calculated to      20S {\text {20S}}       for one to twenty nodes. The coefficients for the threeterm recurrence relation of the first twenty orthogonal polynomials associated with the weight function exp      ( −  x 2 ) ( - {x^2})       on the interval      [ 0 , ∞  ) [0, \infty )       are also tabulated to      20 S 20{\text {S}}      .

Gauss quadrature rules for the evaluation of 2𝜋^{-1/2}∫₀^{∞}exp(-𝑥²)𝑓(𝑥)𝑑𝑥