The characteristic exponent of second-order linear differential equations with two irregular singular points

Bühring, Wolfgang

doi:10.1090/S0002-9939-1993-1169022-6

The characteristic exponent of second-order linear differential equations with two irregular singular points
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Proc. Amer. Math. Soc. 118 (1993), 801-812 Request permission

Abstract:

A second-order linear differential equation with two irregular singular points, of which one has unit rank, is investigated. A simple limit formula is obtained for the characteristic exponent of the multiplicative solutions as well as a more detailed asymptotic formula which is suitable for getting accurate numerical values. Only the recursively known coefficients of the formal power series solutions at the irregular singular point of unit rank enter our formulas.

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