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Zeros of the partial sums of cos (z) and sin (z). I

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Abstract

We extend results of Szegő (1924) and Kappert (1996) on the location of the zeros of the normalized partial sums of cos (z) and sin (z), and their rates of convergence to the associated Szegő curves.

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References

  1. J.D. Buckholtz, A characterization of the exponential series, Part II, Amer. Math. Monthly 73 (1966) 121–123.

    Google Scholar 

  2. A.J. Carpenter, R.S. Varga and J. Waldvogel, Asymptotics for the zeros of the partial sums of ez. I, Rocky Mountain J. Math. 21 (1991) 99–120.

    Google Scholar 

  3. P. Henrici, Applied and Computational Complex Analysis, Vol. 2 (Wiley, New York, 1977).

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  4. M. Kappert, On the zeros of the partial sums of cos(z) and sin(z), Numer. Math. 74 (1996) 397–417.

    Google Scholar 

  5. G. Szegö, Ñber eine Eigenschaft der Exponentialreihe, Sitzungsber. Math. Ges. 23 (1924) 50–64.

    Google Scholar 

  6. E.C. Titchmarsh, The Theory of Functions, 2nd ed. (Oxford Univ. Press, London, 1939).

    Google Scholar 

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Varga, R.S., Carpenter, A.J. Zeros of the partial sums of cos (z) and sin (z). I. Numerical Algorithms 25, 363–375 (2000). https://doi.org/10.1023/A:1016648721367

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  • DOI: https://doi.org/10.1023/A:1016648721367

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