论文标题
关于塞内塔的猜想
On a conjecture of Seneta
论文作者
论文摘要
在此简短说明中，我们证明$h_β（x）=β\ int_0^x y^{β-1} \上线f（y）\ mathrm {d} y $定期与index $ρ\在[0，β）$ in [0，β）$ in [0，β）$时均定期变化，并且仅当$v_β（x）= x（x）= \ int = \ int = \ themm f（y）$定期随着相同的索引而变化。这意味着Seneta最近的猜想的扩展版本。
In this short note we prove that $h_β(x) = β\int_0^x y^{β-1} \overline F(y) \mathrm{d} y$ is regularly varying with index $ρ\in [0,β)$ if and only if $V_β(x) = \int_{[0,x]} y^β\mathrm{d} F(y)$ is regularly varying with the same index. This implies an extended version of a recent conjecture by Seneta.
