A SYSTEM OF INEQUALITIES FOR THE INCOMPLETE GAMMA FUNCTION AND THE NORMAL INTEGRAL

摘要: 1. Introduction and summary. In this paper a new set of inequalities bounds for the incomplete gamma function are obtained. These based on continued fraction expansions (Sections 2 3). Comparisons between two sets some other known made (Section 4). Bounds also obtained Mills' ratio normal integral 5) an analogue 6) distribution. Some applications these to distribution theory problems arising in multiple decision described 6). 2. System -y(a, x) expansion. Let 'y(a, = x ta le t dt. Various authors (see, Khovanskii (1956)) have derived following expansion