# §7.9 Continued Fractions

 7.9.1 $\displaystyle\sqrt{\pi}e^{z^{2}}\operatorname{erfc}z$ $\displaystyle=\cfrac{z}{z^{2}+\cfrac{\frac{1}{2}}{1+\cfrac{1}{z^{2}+\cfrac{% \frac{3}{2}}{1+\cfrac{2}{z^{2}+\cdots}}}}},$ $\Re z>0$, ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\operatorname{erfc}\NVar{z}$: complementary error function, $\mathrm{e}$: base of natural logarithm, $\Re$: 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 and Ch.7 7.9.2 $\displaystyle\sqrt{\pi}e^{z^{2}}\operatorname{erfc}z$ $\displaystyle=\cfrac{2z}{2z^{2}+1-\cfrac{1\cdot 2}{2z^{2}+5-\cfrac{3\cdot 4}{2% z^{2}+9-\cdots}}},$ $\Re z>0$, 7.9.3 $\displaystyle w\left(z\right)$ $\displaystyle=\frac{i}{\sqrt{\pi}}\cfrac{1}{z-\cfrac{\frac{1}{2}}{z-\cfrac{1}{% z-\cfrac{\frac{3}{2}}{z-\cfrac{2}{z-\cdots}}}}},$ $\Im z>0$. ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $w\left(\NVar{z}\right)$: Faddeeva (or Faddeyeva) function, $\Im$: imaginary part, $\mathrm{i}$: imaginary unit 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 and Ch.7