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References

  1. “Bateman Project” (Erdelyi, Magnus, Oberhettinger, Tricomi), Higher Transcendental Functions. III. New York-Toronto-London: McGraw-Hill 1955.

    Google Scholar 

  2. Ince, E.L., The periodic Lamé functions. Proc. Roy. Soc. Edin. 60, 47–63 (1940).

    Google Scholar 

  3. Magnus, W., Infinite Determinants in the Theory of Mathieu's and Hill's Equations. New York University, Institute of Mathematical Sciences, Research Report BR-1 (1953).

  4. Magnus, W., Infinite determinants associated with Hill's equation. Pacific Journal of Math. 5, Suppl. 2, 941–951 (1955).

    Google Scholar 

  5. Magnus, W., & A. Shenitzer, Hill's Equation. Part I: General Theory. New York University, Institute of Mathematical Sciences, Research Report BR-22 (1957).

  6. Magnus, W., & S. Winkler, The Coexistence Problem for Hill's Equation. New York University, Institute of Mathematical Sciences, Research Report BR-26 (1958).

  7. Magnus, W., & S. Winkler, Hill's Equation. New York: Interscience Publishers 1966.

    Google Scholar 

  8. Meixner, J., & F.W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen. Berlin-Göttingen-Heidelberg: Springer 1954.

    Google Scholar 

  9. Mennicken, R., Zur Theorie der Poincaré-Perronschen Differenzengleichungen. Arch. d. Math. 16, 452–464 (1965).

    Google Scholar 

  10. Mennicken, R., Neue numerische Verfahren zur Berechnung des charakteristischen Exponenten der verallgemeinerten Mathieuschen Differentialgleichung (1+2 γ cos 2x) y″ (x)+ (λ-2h 2 cos 2x) y(x)=0. Arch. Rational Mech. Anal. 26, 163–178 (1967).

    Google Scholar 

  11. Schäfke, F.W., Ein Verfahren zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung. I. Numer. Math. 3, 30–36 (1960).

    Google Scholar 

  12. Schäfke, F.W., R. Ebert & H. Groh, Ein Verfahren zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung. II. Numer. Math. 4, 1–7 (1962).

    Google Scholar 

  13. Schäfke, F.W., & D. Schmidt, Ein Verfahren zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung. III. Numer. Math. 8, 68–71 (1966).

    Google Scholar 

  14. Stoss, J., Ein Verfahren zur Berechnung des charakteristischen Exponenten der Differentialgleichung y″(x)+(λ01 cos x+λ 2 cos 2x) y(x) = 0. Numer. Math. 10, 423–436 (1967).

    Google Scholar 

  15. Whittaker, E.T., & G.N. Watson, A Course of Modern Analysis. Cambridge: University Press 1962.

    Google Scholar 

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Communicated by J. Meixner

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Mennicken, R. On Ince's equation. Arch. Rational Mech. Anal. 29, 144–160 (1968). https://doi.org/10.1007/BF00281363

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