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•#0? ^ 2 ? ^8? ^0#2> ö'ofh, ^2^8? ^0#2> # 0 # 8 , #2^3? are of fundamental importance for the arithmetic of class number relations. Two of these. (6), (7) below, have not previously been stated. The expansions of this pair depend upon those of the remaining seven and upon some additional facts concerning representations in a certain ternary quadratic form. The present paper therefore contains the complete set of expansions. In a recent note f the author has shown that the classical series of Kronecker and Hermite, in which all summations are with respect to n = 0 to oo? WW) = *2qF(in + l),

Complete class number expansions for certain elliptic theta constants of the third degree