An asymptotic formula for \(\pi\)
Let \(R_ 0,R_ 1,R_ 2,..\). be a nondegenerate binary linear recurrence of integers defined by \(R_ n=AR_{n-1}+BR_{n-2}\) \((n>1)\), where \(R_ 0\), \(R_ 1=1,and\) A, B are fixed nonzero integers. It is proved that \[ \sqrt{\frac{6\cdot \log | R_ 1\cdot R_ 2\cdot \cdot \cdot R_ N|}{\log [R_ 1,R_ 2,...,R_ N]}}\quad =\quad \pi +O(\frac{1}{\log N}) \] for any sufficiently large integer N ([ ] denotes the least common multiple of numbers).
scientific article; zbMATH DE number 4087744