On a separating solution of a recurrent equation
2007, Volume 12, Number 5, pp. 490-501
Author(s): Sinai Y. G.
Author(s): Sinai Y. G.
We consider the recurrent equation
$\Lambda_p = \frac{1}{p-1} \sum\limits_{p_1=1}^{p-1} f (\frac{p1}{p}) \Lambda_{p_1} ยท \Lambda_{p-p_1}$
which depends on the initial condition $\Lambda_1=x$. Under some conditions on $f$ we show that there exists the value of x for which $\Lambda_p$ tends to a constant as p tends to infinity.
$\Lambda_p = \frac{1}{p-1} \sum\limits_{p_1=1}^{p-1} f (\frac{p1}{p}) \Lambda_{p_1} ยท \Lambda_{p-p_1}$
which depends on the initial condition $\Lambda_1=x$. Under some conditions on $f$ we show that there exists the value of x for which $\Lambda_p$ tends to a constant as p tends to infinity.
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