Some considerations in connection with Kurepa's function

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in the sense of Cauchy's principal value at point \cite{Slavic_70}. In this paper we give an addendum to the proof of Slavi\' c's representation of Kurepa's function $K(z)$ \cite{Slavic_73}. Also, we consider some representations of functions $K(z)$ and $K_{1}(z)$ via incomplete gamma function and we consider differential transcendency of previous functions too.Comment: 11 page

Change in the perception of the poverty line during times of depression : Russia 1993-96

During Russia's economic transition real income declined precipitously for most of the population. How were Russians'perceptions of the minimum income level needed to survive affected by such a rapid decline in their incomes? Based on data collected from repeated surveys of individuals during the period from March 1993 to September 1996, the authors find that the subjective estimate of that minimum income for an adult Russian decreased by about 1.7 percent each month. This sharp reduction in the subjective poverty line meant that proportionately fewer people felt poor. However at all times at least 60 percent of the population considered itself poor. In other words, the percentage of the"subjectively poor"tended to decline as the perception of the needed minimum was reduced. In this somewhat unusual situation, the percentage of the subjectively poor decreased more or less in step with a reduction in people's real income. Only larger-than-usual income decreases were needed to jolt the population - that is, to keep the percentage of the subjectively poor unchanged. The percentage of the self-addressed poor was always lower than the percentage of the poor according to the"social"subjective poverty line. This suggests that pockets of the population regarded their own income as adequate although in the public perception they were poor. This in turn suggests two mechanisms for adapting to worsening circumstances: 1) a reduction in what people perceive to be the minimum income needed for survival and 2) the existence in the population of pockets of people who demand even less than others.Environmental Economics&Policies,Services&Transfers to Poor,Economic Conditions and Volatility,Poverty Impact Evaluation,Poverty Monitoring&Analysis,Environmental Economics&Policies,Inequality,Services&Transfers to Poor,Safety Nets and Transfers,Rural Poverty Reduction