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7 Error Functions, Dawson’s and Fresnel IntegralsProperties

§7.10 Derivatives

7.10.1 dn+1erfzdzn+1=(-1)n2πHn(z)e-z2,
n=0,1,2,.

For the Hermite polynomial Hn(z) see §18.3.

7.10.2 w(z)=-2zw(z)+(2i/π),
7.10.3 w(n+2)(z)+2zw(n+1)(z)+2(n+1)w(n)(z)=0,
n=0,1,2,.
7.10.4 df(z)dz =-πzg(z),
dg(z)dz =πzf(z)-1.