We present a fast and exact algorithm to compute maximum likelihood estimates for the number of faults initially contained in a software, using the hypergeometric software reliability model. The algorithm is based on a rigorous mathematical analysis of the growth behavior of the likelihood function for the model. We also clarify the stochastic process underlying the model and prove a recursion ...

In [16], the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) a...

An algebraically motivated generalization of Gosper’s algorithm to indefinite bibasic hypergeometric summation is presented. In particular, it is shown how Paule’s concept of greatest factorial factorization of polynomials can be extended to the bibasic case. It turns out that most of the bibasic hypergeometric summation identities from literature can be proved and even found this way. A Mathem...

Abstract. We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Our lower bounds are asymptotically precise at x = 0, while the upper bounds are either asymptotically precise or at least agree with q+1Fq((aq+1), (bq);−x) at x = ∞. Inequalities are derived as corollaries of a theorem asserting the monotony...