Ultra power and ultra exponential functions

  title={Ultra power and ultra exponential functions},
  author={M. H. Hooshmand},
  journal={Integral Transforms and Special Functions},
  pages={549 - 558}
  • M. Hooshmand
  • Published 1 August 2006
  • Mathematics
  • Integral Transforms and Special Functions
Supposing that a is a positive real number, then for each natural number n, the notation a n is called a to the ultra power of n , and we define by In the other words, , n times. In [Euler, L., De formulis exponentialibus replicatus, Acta Academiac Petropolitenae, 1, 38–60.] the necessary and sufficient condition for the convergence of lim n→∞ a n is proved by Euler and in [Baker, I.N. and Rippon, P.J., 1983, Convergence of infinite exponentials. Annales Academiac Scentiarium Fennicae… 
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De formulis exponentialibus replicatus
  • Acta Academiac Petropolitenae
  • 1777