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 Infinite products andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 04/06/2009, 09:20 AM 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 $x=(-1)$ we have $ \text{tet}(x) = \sum_{k=0}^{\infty}c_k(x+1)^k$ and using the definition, we can rewrite this as $ \begin{array}{rl} \text{tet}(x) & = \exp\left(\text{tet}(x-1)\right) \\ & = \exp\left(\sum_{k=0}^{\infty}c_kx^k\right) \\ & = \prod_{k=0}^{\infty} \exp(c_k{x^k}) \\ & = \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? Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Infinite products - by andydude - 04/06/2009, 09:20 AM RE: Infinite products - by tommy1729 - 04/06/2009, 09:38 PM RE: Infinite products - by bo198214 - 04/06/2009, 09:55 PM

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