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Improving convergence of Andrew's slog
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 quickfur Wrote:the idea of an extension of tetration to real numbers that is both \( C^{\infty} \) and satisfies \( x[4]y = x^{x[4](y-1)} \) for all real y really appeals to me. Not only \( C^{\infty} \) but even analtytic! However still this does not determine the function ... there are other choices as you can read somewhere through the forum  *which I see you do already extensively*
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