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A new approximation is given for      ∫  x ∞  e −  t 2 / 2 t p d t \smallint _x^\infty {e^{ - {t^2}/2}{t^p}dt}      ,      x &gt; 0 x &gt; 0      ,  p  real, which extends an earlier approximation of Boyd’s for      p = 0 p = 0      .

An approximation for ∫^{∞}ᵪ𝑒^{-𝑡2/2}𝑡^{𝑝}𝑑𝑡, 𝜒>0, 𝑝 real