\[R_{n}^{(\mathrm{f})}(z)=\frac{(-1)^{n}}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{e^{%
-\pi z^{2}t/2}t^{2n-(1/2)}}{t^{2}+1}\,\mathrm{d}t,\]