Research On A Generating Function Associating With Record Time

This paper firstly outlines the research of the record value in recent years. By studying the distribution of record time, we obtained the generating function of record time. Due to the most research for the record value and the record time associating with the expansion the paper deal with fi,j(k) by analogizing the research methods of the first kind stirling number. We discussed its recursive relationship and how to expressed it through the stirling number separately, and its single peak and congruence were discussed.