Digital Library of Mathematical Functions
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7 Error Functions, Dawson’s and Fresnel IntegralsProperties

§7.9 Continued Fractions

7.9.1 πz2erfcz =zz2+121+1z2+321+2z2+,
z>0,
7.9.2 πz2erfcz =2z2z2+1-122z2+5-342z2+9-,
z>0,
7.9.3 w(z) =π1z-12z-1z-32z-2z-,
z>0.

See also Cuyt et al. (2008, pp. 255–260, 263–267, 270–273).