Geodesic
Confluence of Fuchsian second-order differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 2, pp. 233-247 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Ordinary linear homogeneous second-order differential equations with polynomial coefficients including one in front of the second derivative are studied. Fundamental definitions for these equations: of $s$-rank of the singularity (different from Poincaré rank), of $s$-multisymbol of the equation and of $s$-homotopic transformations are proposed. Generalization of Fuchs\rq theorem for confluent Fuchsian equations is proved. The tree structure of types of equations is exposed and the generalized confluence theorem is proved. 
@article{TMF_1995_104_2_a2,
     author = {A. Seeger and W. Lay and S. Yu. Slavyanov},
     title = {Confluence of {Fuchsian} second-order differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {233--247},
     year = {1995},
     volume = {104},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_104_2_a2/}
}
TY  - JOUR
AU  - A. Seeger
AU  - W. Lay
AU  - S. Yu. Slavyanov
TI  - Confluence of Fuchsian second-order differential equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 233
EP  - 247
VL  - 104
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_104_2_a2/
LA  - ru
ID  - TMF_1995_104_2_a2
ER  - 
%0 Journal Article
%A A. Seeger
%A W. Lay
%A S. Yu. Slavyanov
%T Confluence of Fuchsian second-order differential equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 233-247
%V 104
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1995_104_2_a2/
%G ru
%F TMF_1995_104_2_a2
A. Seeger; W. Lay; S. Yu. Slavyanov. Confluence of Fuchsian second-order differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 2, pp. 233-247. http://geodesic.mathdoc.fr/item/TMF_1995_104_2_a2/

[1] Ince E. L., Ordinary Differential Equations, Dover Publications, New York, 1959 | MR

[2] Moon P., Spencer D. E., Field Theory Handbook, Springer-Verlag, Berlin–Heidelberg–New York, 1971 | MR

[3] Forsyth A. R., Theory of Differential Equations, Dover Publications, New York, 1959 | MR | Zbl

[4] Whittaker E. T., Watson G. N., A Course of Modern Analysis, University Press, Cambridge, 1963 | MR

[5] Fuchs L., J. reine und angew. Math., 66 (1866), 121–160 | DOI | MR

[6] Bieberbach L., Theorie der gewöhnlichen Differentialgleichungen, Springer-Verlag, Berlin–Göttingen–Heidelberg–New York, 1965 | MR | Zbl

[7] Decarreau A., Dumont-Lepage M. C., Maroni P., Robert A., Ronveaux A., Ann. Soc. Sci. de Bruxelle, 92 (1978), 53–78 | MR | Zbl

[8] Lay W., Seeger A., Slavyanov S. Yu., A Classification Scheme of Heun\rq s Differential Equation and its Confluent Cases (to appear)