Edward Omey - Dept. MEES, Campus Brussels, KU Leuven, Warmoesberg ۲۶, Brussels, Belgium.
Meitner Cadena - DECE, Universidad de las Fuerzas Armadas, Sangolqui, Ecuador.

Considering slowly varying functions (SVF), %Seneta (۲۰۱۹) Seneta in ۲۰۱۹ conjectured the following implication, for \alpha\geq۱,\int_۰^x y^{\alpha-۱}(۱-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{۰}^x y^{\alpha}dF(y)\textrm{\ is SVF, as x\to\infty,}where F(x) is a cumulative distribution function on [۰,\infty). By applying the Williamson transform, an extension of this conjecture is proved. Complementary results related to this transform and particular cases of this extended conjecture are discussed.

Regular variation, De Haan class, Truncated moments, Williamson transform