The expansion of Kummer’s hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable. The error performed approximating the Kummer function with a finite sum of Gammas is evaluated analytically. Bounds for it are derived, both pointwisely and uniformly in the variable; these characterize the convergence rate of the serie...

Abstract A new lifetime distribution has been defined. This is obtained from a transformation of random variable with beta and called here the kagebushin-beta distribution. Some mathematical properties such as mode, quantile function, ordinary incomplete moments, mean deviations over median entropies Rényi Shannon are demonstrated. The maximum likelihood method used to obtain parameter estimate...

The incomplete gamma function and incomplete beta function are important special functions in statistics. In modern theory of special functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles [1, Chap 2]. However, domains of integrations of these incomplete functions are not cycles. Solutions of A-hypergeometric systems ([3], [7, p.221]) have integral repr...

We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform expansion by applying techniques used for the existing uniform expansions for (...