Asymptotic expansions for ratios of products of gamma functions

An asymptotic expansion for a ratio of products of gamma functions is derived.Comment: 6 pages. v2: A paragraph containing one additional reference included at the end. Some trivial errors correcte

Second-order linear differential equations with two irregular singular points of rank three: the characteristic exponent

For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the characteristic exponent of the multiplicative solutions. The Stokes multipliers are represented by converging series with terms for which limit formulas as well as more detailed asymptotic expansions are available. Here certain new, recursively known coefficients enter, which are closely related to but different from the coefficients of the formal solutions at one of the irregular singular points of the differential equation. The coefficients of the formal solutions then appear as finite sums over subsets of the new coefficients. As a by-product, the leading exponential terms of the asymptotic behaviour of the late coefficients of the formal solutions are given, and this is a concrete example of the structural results obtained by Immink in a more general setting. The formulas displayed in this paper are not of merely theoretical interest, but they also are complete in the sense that they could be (and have been) implemented for computing accurate numerical values of the characteristic exponent, although the computational load is not small and increases with the rank of the singular point under consideration.Comment: 33 page

Failure in generating hemopoietic stem cells is the primary cause of death from cytomegalovirus disease in the immunocompromised host

We have shown in a murine model system for cytomegalovirus (CMV) disease in the immunocompromised host that CMV infection interferes with the earliest detectable step in hemopoiesis, the generation of the stem cell CFU-S-I, and thereby prevents the autoreconstitution of bone marrow after sublethal irradiation. The antihemopoietic effect could not be ascribed to a direct infection of stem cells. The failure in hemopoiesis was prevented by adoptive transfer of antiviral CD8+ T lymphocytes and could be overcome by syngeneic bone marrow transplantation. CD8+ T lymphocytes and bone marrow cells both mediated survival, although only CD8+ T lymphocytes were able to limit virus multiplication in host tissues. We concluded that not the cytopathic effect of virus replication in host tissues, but the failure in hemopoiesis, is the primary cause of death in murine CMV disease

© Hindawi Publishing Corp. ASYMPTOTIC EXPANSIONS FOR RATIOS OF PRODUCTS OF GAMMA FUNCTIONS

An asymptotic expansion for a ratio of products of gamma functions is derived