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Convergent Liouville-Green Expansions for Second-Order Linear Differential Equations, with an Application to Bessel Functions

T. M. Dunster, D. A. Lutz and R. Schafke
Proceedings: Mathematical and Physical Sciences
Vol. 440, No. 1908 (Jan. 8, 1993), pp. 37-54
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52301
Page Count: 18
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Convergent Liouville-Green Expansions for Second-Order Linear Differential Equations, with an Application to Bessel Functions
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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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