ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIII, 1 (2004)
p. 75 – 87
Effective Asymptotics for Some
Nonlinear Recurrences and Almost Doubly-Exponential Sequences
E. Ionascu and P. Stanica
Abstract.
We develop a technique to compute asymptotic expansions for
recurrent sequences of the form $a_{n+1}=f(a_n)$, where
$f(x)=x-ax^{\alpha}+bx^{\beta} +o(x^{\beta})$ as $x\rightarrow 0$,
for some real numbers $\alpha, \beta$, $a$, and $b$ satisfying
$a>0$, $1<\ALPHA<\BETA {3\SQRT{3}\OVER10}{\LN WE APPLY E ASSUMPTIONS, ALMOST THE PROVE QUART. NAMELY THAT INSTANCE, SLOANE OF [FIBONACCI [AMER. CAN TECHNIQUE, DOUBLY-EXPONENTIAL, $A_N$ FORMULA: 11 ONE FOR $A_N="\lfloor{k^{2^n}+\frac{5}{2}}\rfloor$" \RR$. TECHNICAL CONSIDER WHICH NUMBER REAL EXPANSIONS $K$, MOREOVER, SOLUTION N^2\SQRT{N}} WHERE $A_1\IN SUMMARIZES IS $3034[1984,58]$, N N\OVER $. N\SQRT{N}}+{9\SQRT{3}\OVER TO RESULT
AMS Subject classification: 11B37, 11B83, 11K31, 11Y55, 34E05, 35C20, 40A05.
Keywords:
Sequences, Dynamics, Asymptotic Expansions, Doubly-Exponential.
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