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TMF, 1995, Volume 104, Number 2, Pages 233–247 (Mi tmf1334)  

This article is cited in 6 scientific papers (total in 6 papers)

Confluence of Fuchsian second-order differential equations

A. Seeger, W. Lay, S. Yu. Slavyanov

Saint-Petersburg State University

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1995, 104:2, 950–960

Bibliographic databases:

Received: 25.10.1994

Citation: A. Seeger, W. Lay, S. Yu. Slavyanov, “Confluence of Fuchsian second-order differential equations”, TMF, 104:2 (1995), 233–247; Theoret. and Math. Phys., 104:2 (1995), 950–960

Citation in format AMSBIB
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\by A.~Seeger, W.~Lay, S.~Yu.~Slavyanov
\paper Confluence of Fuchsian second-order differential equations
\jour TMF
\yr 1995
\vol 104
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\pages 233--247
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1488672}
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\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 2
\pages 950--960
\crossref{https://doi.org/10.1007/BF02065975}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Ya. Kazakov, S. Yu. Slavyanov, “Integral relations for special functions of hypergeometric and Heun class”, Theoret. and Math. Phys., 107:3 (1996), 733–739  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. N. A. Veshev, “Degeneration of solutions of Heun's equation under fusion of singularities”, Theoret. and Math. Phys., 110:2 (1997), 179–182  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. Yu. Slavyanov, “Structural theory of special functions”, Theoret. and Math. Phys., 119:1 (1999), 393–406  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. Yu. Slavyanov, “Recurrent calculations of multipole matrix elements”, Theoret. and Math. Phys., 120:3 (1999), 1213–1219  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. Yu. Slavyanov, “Isomonodromic deformations of Heun and Painlevé equations”, Theoret. and Math. Phys., 123:3 (2000), 744–753  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Tarasov, VF, “The Heun-Schrodinger radial equation with two auxiliary parameters for H-like atoms”, Modern Physics Letters B, 16:25 (2002), 937  crossref  mathscinet  zmath  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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