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

Bottlenecks and broomsticks:The molecular evolution of Mycobacterium bovis

Mycobacterium bovis is the cause of tuberculosis in cattle and is a member of the Mycobacterium tuberculosis complex. In contrast to many other pathogenic bacterial species, there is little evidence for the transfer and recombination of genes between cells. The clonality of this group of organisms indicates that the population structure is dominated by reductions in diversity, caused either by population bottlenecks or selective sweeps as entire chromosomes become fixed in the population. We describe how these forces have shaped not only the phylogeny of this group but also, at a very local level, the population structure of Mycobacterium bovis in the British Isles. We also discuss the practical implications of applying this knowledge to understanding the spread of infection and the development of improved vaccines and diagnostic test