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7 Error Functions, Dawson’s and Fresnel IntegralsProperties

§7.11 Relations to Other Functions

Incomplete Gamma Functions and Generalized Exponential Integral

Confluent Hypergeometric Functions

For the notation see §13.2(i).

7.11.4 erfz=2zπM(12,32,z2)=2zπez2M(1,32,z2),
7.11.5 erfcz=1πez2U(12,12,z2)=zπez2U(1,32,z2).
7.11.6 C(z)+iS(z)=zM(12,32,12πiz2)=zeπiz2/2M(1,32,12πiz2).

Generalized Hypergeometric Functions