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\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r3124736 = 1.0;
        double r3124737 = k;
        double r3124738 = sqrt(r3124737);
        double r3124739 = r3124736 / r3124738;
        double r3124740 = 2.0;
        double r3124741 = atan2(1.0, 0.0);
        double r3124742 = r3124740 * r3124741;
        double r3124743 = n;
        double r3124744 = r3124742 * r3124743;
        double r3124745 = r3124736 - r3124737;
        double r3124746 = r3124745 / r3124740;
        double r3124747 = pow(r3124744, r3124746);
        double r3124748 = r3124739 * r3124747;
        return r3124748;
}

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))