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Perturbation at an irregular singular point

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Japan-United States Seminar on Ordinary Differential and Functional Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 243))

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Bibliography

  1. G. D. Birkhoff, Singular points of ordinary linear differential equations, Trans. Amer. Math. Soc., 10(1909) 436–470

    Article  MathSciNet  MATH  Google Scholar 

  2. G. D. Birkhoff, Equivalent singular points of ordinary linear differential equations, Math. Ann., 74 (1913) 134–139

    Article  MathSciNet  MATH  Google Scholar 

  3. F. R. Gantmacher, The theory of matrices, II, Chelsea Publ. Co., 1959

    Google Scholar 

  4. E. Hiller, Lectures on ordinary differential equations, Addison-Wesley, 1969

    Google Scholar 

  5. P. F. Hsieh and Y. Sibuya, Note on regular perturbations of linear ordinary differential equations at irregular singular points, Funk. Ekva., 8 (1966) 99–108

    MathSciNet  MATH  Google Scholar 

  6. M. Hukuhara, Sur les points singuliers des équations différentielles linéaries, II and III, J. Fac. Sci., Hokkaido Univ., 5 (1937) 157–166 and Mem. Fac. Sci., Kyushu Univ., 2 (1942) 125–137

    Google Scholar 

  7. M. Kukuhara, Sur les équations différentielles linéaires à coefficients périodiques et contenant un paramètre, J. Fac. Sci., Univ. Tokyo, Sec. I, 7 (1954) 69–85

    Google Scholar 

  8. D. A. Lutz, Linear perturbations of irregular singular systems, Proc. U.S.-Japan Seminar on Diff. and Func. Equations, Benjamin, 1967, 555–558.

    Google Scholar 

  9. D. A. Lutz, Perturbations of matrix differential equations in the neighborhood of a singular point, Funk. Ekva., 13 (1970) 97–107

    MathSciNet  MATH  Google Scholar 

  10. J. Malmquist, Sur l'étude analytique des solutions d'un système d'équation différentielles dans le voisinage d'un point singulier d'indétermination, I, II and III, Acta Math., 73 (1940) 87–129, 74 (1941) 1–64 and 74 (1941) 109–128

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Masani, On a result of G. D. Birkhoff on linear differential systems, Proc. Amer. Math. Soc., 10 (1959) 696–698

    Article  MathSciNet  MATH  Google Scholar 

  12. F. E. Mullin, On the regular perturbation of the subdominant solution to second order linear ordinary differential equations with polynomial coefficients, Funk. Ekva., 11 (1968) 1–38

    MathSciNet  MATH  Google Scholar 

  13. T. Saito, On a singular point of a second order linear differential equation containing a parameter, Funk. Ekva., 5 (1963) 1–29

    MathSciNet  MATH  Google Scholar 

  14. Y. Sibuya, Simplification of a system of linear ordinary differential equations about a singular point, Funk Ekva., 4 (1962) 29–56

    MathSciNet  MATH  Google Scholar 

  15. Y. Sibuya, Perturbation of linear ordinary differential equations at irregular singular points, Funk. Ekva., II (1968) 235–246

    MathSciNet  MATH  Google Scholar 

  16. H. L. Turrittin, Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Acta Math. 93 (1955) 27–66

    Article  MathSciNet  MATH  Google Scholar 

  17. H. L. Turrittin, Reduction of ordinary differential equations to the Birkhoff canonical form, Trans. Amer. Math. Soc., 107 (1963) 485–507

    Article  MathSciNet  MATH  Google Scholar 

  18. W. Wasow, Asymptotic expansions for ordinary differential equations, Interscience, 1965

    Google Scholar 

  19. F. Zernike, Eine asymptotische Entwicklung für die grösste Nullstelle der Hermiteschen Polynome, Koninklijke Akademie van Wetenschappen te Amsterdam, Proc. of the Section of Sci., 34 (1931) 673–680.

    MATH  Google Scholar 

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Authors
  1. Yasutaka Sibuya
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Minoru Urabe

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© 1971 Springer-Verlag

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Sibuya, Y. (1971). Perturbation at an irregular singular point. In: Urabe, M. (eds) Japan-United States Seminar on Ordinary Differential and Functional Equations. Lecture Notes in Mathematics, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058725

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  • DOI: https://doi.org/10.1007/BFb0058725

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05708-6

  • Online ISBN: 978-3-540-37080-2

  • eBook Packages: Springer Book Archive

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