# §7.9 Continued Fractions

 7.9.1 $\displaystyle\sqrt{\pi}e^{z^{2}}\mathop{\mathrm{erfc}\/}\nolimits z$ $\displaystyle=\cfrac{z}{z^{2}+\cfrac{\frac{1}{2}}{1+\cfrac{1}{z^{2}+\cfrac{% \frac{3}{2}}{1+\cfrac{2}{z^{2}+\cdots}}}}},$ $\Re{z}>0$, Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathop{\mathrm{erfc}\/}\nolimits\NVar{z}$: complementary error function, $\mathrm{e}$: base of exponential function, $\Re{}$: real part and $z$: complex variable A&S Ref: 7.1.14 (in different form) Referenced by: §7.9 Permalink: http://dlmf.nist.gov/7.9.E1 Encodings: TeX, pMML, png See also: Annotations for 7.9 7.9.2 $\displaystyle\sqrt{\pi}e^{z^{2}}\mathop{\mathrm{erfc}\/}\nolimits z$ $\displaystyle=\cfrac{2z}{2z^{2}+1-\cfrac{1\cdot 2}{2z^{2}+5-\cfrac{3\cdot 4}{2% z^{2}+9-\cdots}}},$ $\Re{z}>0$, 7.9.3 $\displaystyle\mathop{w\/}\nolimits\!\left(z\right)$ $\displaystyle=\frac{i}{\sqrt{\pi}}\cfrac{1}{z-\cfrac{\frac{1}{2}}{z-\cfrac{1}{% z-\cfrac{\frac{3}{2}}{z-\cfrac{2}{z-\cdots}}}}},$ $\Im{z}>0$. Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathop{w\/}\nolimits\!\left(\NVar{z}\right)$: complementary error function, $\Im{}$: imaginary part and $z$: complex variable A&S Ref: 7.1.15 (in different form) Permalink: http://dlmf.nist.gov/7.9.E3 Encodings: TeX, pMML, png See also: Annotations for 7.9