• Corpus ID: 233024768

The Limits of a Family; of Asymptotic Solutions to The Tetration Equation

  title={The Limits of a Family; of Asymptotic Solutions to The Tetration Equation},
  author={James David Nixon},
  • J. Nixon
  • Published 1 April 2021
  • Mathematics
In this paper we construct a family of holomorphic functions βλ(s) which are solutions to the asymptotic tetration equation. Each βλ satisfies the functional relationship βλ(s+ 1) = eλ e−λs + 1 ; which asymptotically converges as log βλ(s+1) = βλ(s)+O(e) as <(λs)→∞. This family of asymptotic solutions is used to construct a holomorphic function tetβ(s) : C/(−∞,−2]→ C such that tetβ(s+ 1) = eβ and tetβ : (−2,∞)→ R bijectively. 
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