Infinite products

[bo198214]

\(
\begin{array}{rl}
\text{tet}(x) =
\dots & = \prod_{k=0}^{\infty} a_k^{x^k} \\
\end{array}
\)

where \( a_k = e^{c_k} \)

I wonder if this simplifies the coefficients or just makes things more complicated?

To calculate the coefficients you either need on both sides a product or on both sides a sum. So I dont see how the product representation can be useful.