# ANALYTIC PROPERTIES OF THE LIMITS OF THE EVEN AND ODD HYPERPOWER SEQUENCES

• Cho, Yun-Hi (Department Of Mathematics, University Of Seoul) ;
• Kim, Young-One (Department Of Mathematical Sciences, Seoul National University)
• Published : 2004.02.01
• 123 22

#### Abstract

Let he(x) and $h_{o}(x)$ denote the limits of the sequences $\{^{2n}x\}\;and\;\{^{2n+1}x\}$, respectively. Asymptotic formulas for the functions E\$h_e\;and\;h_o$ at the points $e^{-e}$ and 0 are established.

#### References

1. Reading Complex Analysis S.Lang
2. Amer. Math. Monthly v.88 Exponentials reiterated R.A.Knoebel https://doi.org/10.2307/2320546
3. An Introduction to Mathematical Analysis(2nd edtion) J.Lewin;M.Lewin
4. Amer. Math. Monthly v.92 A note on complex iteration I.N.Baker;P.J.Rippon https://doi.org/10.2307/2322513
5. Amer. Math. Monthly v.93 The interval of convergence and limiting functions of a hyperpower sequence J. M. De Villiers;P.N.Robinson https://doi.org/10.2307/2322537
6. Amer. Math. Monthly v.108 Inverse functions of y=$x^{1/x}$ Y.Cho;K.Park https://doi.org/10.2307/2695417
7. Asymptotic Methods in Analysis N. G. de Bruijn