Separating Solution of a Quadratic Recurrent Equation

Yakov G. Sinai, Ilya Vinogradov

In this paper we consider the recurrent equation $${\Lambda }_{p+1}=\frac{1}{p}\sum _{q=1}^{p}f\left(\frac{q}{p+1}\right){\Lambda }_q{\Lambda }_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and ${\Lambda }_1=y>0$ given. We giv…