In this paper, it says that the three Borwein cubic theta functions obey the identity $a(q)^{3}=b(q)^{3}+c(q)^{3}$, which is strongly reminiscent of the identity that Dixonian elliptic functions obey $\mathrm{sm}^{3}(z)+\mathrm{cm}^{3}(z)=1$. What relationship (if any) exists between the Dixonian elliptic functions and the Borwein cubic theta functions?
2026-03-26 10:59:44.1774522784
Relationship between Dixonian elliptic functions and Borwein cubic theta functions
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