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8 Incomplete Gamma and Related FunctionsIncomplete Gamma Functions

§8.5 Confluent Hypergeometric Representations

For the confluent hypergeometric functions M, M, U, and the Whittaker functions Mκ,μ and Wκ,μ, see §§13.2(i) and 13.14(i).

8.5.1 γ(a,z)=a-1zae-zM(1,1+a,z)=a-1zaM(a,1+a,-z),
a0,-1,-2,.
8.5.2 γ*(a,z)=e-zM(1,1+a,z)=M(a,1+a,-z).
8.5.3 Γ(a,z)=e-zU(1-a,1-a,z)=zae-zU(1,1+a,z).
8.5.4 γ(a,z)=a-1z12a-12e-12zM12a-12,12a(z).
8.5.5 Γ(a,z)=e-12zz12a-12W12a-12,12a(z).