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I just remembered a method I tried like 5 years ago, but haven't visited in a while.
Now that we have better power series expansions of tetration, for example, at
)
we have
and using the definition, we can rewrite this as
where
I wonder if this simplifies the coefficients or just makes things more complicated?
Andrew Robbins
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andydude Wrote:I just remembered a method I tried like 5 years ago, but haven't visited in a while.
Now that we have better power series expansions of tetration, for example, at we have
and using the definition, we can rewrite this as
where
I wonder if this simplifies the coefficients or just makes things more complicated?
Andrew Robbins
that could have been my own post
i wondered about it too.
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Joined: Aug 2007
andydude Wrote:
where
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.
 = \sum_{k=0}^{\infty}c_k(x+1)^k<br />
)
and using the definition, we can rewrite this as <br />
& = \exp\left(\text{tet}(x-1)\right) \\<br />
& = \exp\left(\sum_{k=0}^{\infty}c_kx^k\right) \\<br />
& = \prod_{k=0}^{\infty} \exp(c_k{x^k}) \\<br />
& = \prod_{k=0}^{\infty} a_k^{x^k} \\<br />
\end{array}<br />
)
where 
