andydude Wrote:hyper4geek Wrote:TetraExp[x] == TetraExpPrime[x] / TetraExpPrime[x-1]
TetraExp[x] == ProductLog[TetraExpPrime[x+1] / TetraExpPrime[x-1]]
But until I can derive the second formula, I'll assume that it's magic
Its quite easily derived
\( \text{TetraExpPrime}[x+1] / \text{TetraExpPrime}[x-1]=\left({}^{x+1}e\right)\left( {}^x e\right)=\left(e^{{}^x e}\right)\left({}^xe\right) \) by the first formula.
But W is the inverse function of \( xe^x \) so \( W(ye^y)=y \), then let \( y={}^xe \) and you have it.
PS: Thanks a lot for this seminar presentation. *Always wonders where from Andrew gets his information*
