Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z=1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added several references, added comparison to other methods, and added discussion of recursion stabilit

Dual use of Medicare and the Veterans Health Administration: are there adverse health outcomes?

BACKGROUND: Millions of veterans are eligible to use the Veterans Health Administration (VHA) and Medicare because of their military service and age. This article examines whether an indirect measure of dual use based on inpatient services is associated with increased mortality risk. METHODS: Data on 1,566 self-responding men (weighted N = 1,522) from the Survey of Assets and Health Dynamics among the Oldest Old (AHEAD) were linked to Medicare claims and the National Death Index. Dual use was indirectly indicated when the self-reported number of hospital episodes in the 12 months prior to baseline was greater than that observed in the Medicare claims. The independent association of dual use with mortality was estimated using proportional hazards regression. RESULTS: 96 (11%) of the veterans were classified as dual users. 766 men (50.3%) had died by December 31, 2002, including 64.9% of the dual users and 49.3% of all others, for an attributable mortality risk of 15.6% (p < .003). Adjusting for demographics, socioeconomics, comorbidity, hospitalization status, and selection bias at baseline, as well as subsequent hospitalization for ambulatory care sensitive conditions, the independent effect of dual use was a 56.1% increased relative risk of mortality (AHR = 1.561; p = .009). CONCLUSION: An indirect measure of veterans' dual use of the VHA and Medicare systems, based on inpatient services, was associated with an increased risk of death. Further examination of dual use, especially in the outpatient setting, is needed, because dual inpatient and dual outpatient use may be different phenomena

Inflammatory resolution: New opportunities for drug discovery

Treatment of inflammatory diseases today is largely based on interrupting the synthesis or action of mediators that drive the host’s response to injury. Non-steroidal anti-inflammatories, steroids and antihistamines, for instance, were developed on this basis. Although such small-molecule inhibitors have provided the main treatment for inflammatory arthropathies and asthma, they are not without their shortcomings. This review offers an alternative approach to the development of novel therapeutics based on the endogenous mediators and mechanisms that switch off acute inflammation and bring about its resolution. It is thought that this strategy will open up new avenues for the future management of inflammation-based diseases

The genesis and early developments of Aitken\u2019s process, Shanks\u2019 transformation, the \u3b5\u2013algorithm, and related fixed point methods

In this paper, we trace back the genesis of Aitken\u2019s \u3942 process and Shanks\u2019 sequence transformation. These methods, which are extrapolation methods, are used for accelerating the convergence of sequences of scalars, vectors, matrices, and tensors. They had, and still have, many important applications in numerical analysis and in applied mathematics. They are related to continued fractions and Pad\ue9 approximants. We go back to the roots of these methods and analyze the original contributions. New and detailed explanations on the building and properties of Shanks\u2019 transformation and its kernel are provided. We then review their historical algebraic and algorithmic developments. We also analyze how they were involved in the solution of systems of linear and nonlinear equations, in particular in the methods of Steffensen, Pulay, and Anderson. Testimonies by various actors of the domain are given. The paper can also serve as an introduction to this domain of numerical analysis