The case d=8 is special since it is even but has odd class number h(−d)=1. Given the Kronecker symbol (−dm), we propose a symmetrical closed-form
K(k8)=√2π161√U2(√U2−12+√U2+12)2(8∏m=1[Γ(m8)](−8m))1/2=√2π161√U2(√U2−12+√U2+12)2(Γ(18)Γ(38)Γ(58)Γ(78))1/2
with fundamental unit U2=1+√2 and form reminiscent of the odd d with class number 1.
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