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A connection problem for a regular and an irregular singular point of complex ordinary differential equations
Ist Teil von
SIAM journal on mathematical analysis, 1984-03, Vol.15 (2), p.253-271
Ort / Verlag
Philadelphia, PA: Society for Industrial and Applied Mathematics
Erscheinungsjahr
1984
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
In recent papers [SIAM J. Math. Anal., 11 (1980), pp. 848-862, 863-875] D. Schmidt and the author studied the connection problem for two neighboring regular singular points for quite general linear complex ordinary differential equations. In the present paper these results are generalized in the case that one singular point is irregular singular, but of rank 1 and the leading matrix has $n$ distinct eigenvalues; one singular point is regular singular; and there may be several other singular points. The main result is a limit formula for those connection coefficients which are essential in some specified way. An application to the generalized Heun equation is given.