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On The Tails of the Exponential Series

Published online by Cambridge University Press:  20 November 2018

C. Yalçin Yildirim*
Affiliation:
Department of Mathematics, Bilkent University Ankara 06533 Turkey
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Abstract

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A relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Buckholtz, J. D., A characterization of the exponential series, Amer. Math. Monthly (2) 73(1966), 121123.Google Scholar
2. Conrey, J. B. and Ghosh, A., Zeros of derivatives of the Riemann zeta-function near the critical line, Analytic Number Theory, (éd. et al. Berndt), Progr. Math. 85, Birkhauser Boston, 1990.Google Scholar
3. Conrey, J. B. and Ghosh, A., On the zeros of the Taylor polynomials associated with the exponential function, Amer. Math. Monthly 95(1988), 528533.Google Scholar
4. Dieudonné, J., Sur les zéros des polynômes-sections de ex , Bull. Sci. Math. 70(1935), 333351.Google Scholar
5. Fettis, H. E., Caslin, J. C. and Cramer, K. R., Complex zeros of the error function and of the complementary error function, Math. Comp. 27(1973), 401404.Google Scholar
6. Koosis, P., The Logarithmic Integral I, Cambridge, 1988.Google Scholar
7. Newman, D. J. and Rivlin, T. J., The zeros of the partial sums of the exponential function, J. Approx. Theory 5(1972), 404412; Correction J. Approx. Theory 16(1976), 299300.Google Scholar
8. Soni, K. and Soni, R. P., An approximation connected with the exponential function, Proc. Amer. Math. Soc. (4) 114(1992), 909918.Google Scholar
9. Sos, V. T. and Turân, P., On some new theorems in the theory of Diophantine approximations, Acta Math. Hungar. 6(1955), 241255.Google Scholar
10. Szegô, G., Ubereine eigenschaftder Exponentialreihe, Sitzungsber. Berlin Math. Ges. 23(1924), 5064.Google Scholar
11. Yildinm, C. Y., The mean value of at the zeros of Z(k)(t), C. R. Math. Rep. Acad. Sci. Canada (4) XII( 1990), 135140.Google Scholar
12. Yildinm, C. Y., A sum over the zeros of partial sums of ex , J. Ramanujan Math. Soc. 6(1991 ), 5166.Google Scholar
13. Yildinm, C. Y., On the zeros of the sections of the exponential function, Turk. J. Math. (3) 16(1992), 177182.Google Scholar