Abstract
A class of second-order linear differential equations with a large parameter
u
is considered. It is shown that Liouville–Green type expansions for solutions can be expressed using factorial series in the parameter, and that such expansions converge for Re (
u
) > 0, uniformly for the independent variable lying in a certain subdomain of the domain of asymptotic validity. The theory is then applied to obtain convergent expansions for modified Bessel functions of large order.
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