Geodesic
On the Zeros of Power Series with Exponential Logarithmic Coefficients
Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 257-271

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we investigate the zeros of power series 1 for some functions of coefficients A. In particular, we derive upper and lower bounds for the number of zeros of f in its domain of analyticity. 
Gawronski, W.; Stadtmüller, U. On the Zeros of Power Series with Exponential Logarithmic Coefficients. Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 257-271. doi: 10.4153/CMB-1981-042-1
@article{10_4153_CMB_1981_042_1,
     author = {Gawronski, W. and Stadtm\"uller, U.},
     title = {On the {Zeros} of {Power} {Series} with {Exponential} {Logarithmic} {Coefficients}},
     journal = {Canadian mathematical bulletin},
     pages = {257--271},
     year = {1981},
     volume = {24},
     number = {3},
     doi = {10.4153/CMB-1981-042-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-042-1/}
}
TY  - JOUR
AU  - Gawronski, W.
AU  - Stadtmüller, U.
TI  - On the Zeros of Power Series with Exponential Logarithmic Coefficients
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 257
EP  - 271
VL  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-042-1/
DO  - 10.4153/CMB-1981-042-1
ID  - 10_4153_CMB_1981_042_1
ER  - 
%0 Journal Article
%A Gawronski, W.
%A Stadtmüller, U.
%T On the Zeros of Power Series with Exponential Logarithmic Coefficients
%J Canadian mathematical bulletin
%D 1981
%P 257-271
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-042-1/
%R 10.4153/CMB-1981-042-1
%F 10_4153_CMB_1981_042_1

[1] 1. Ford, W., Studies on divergent series and summability and the asymptotic developments of functions defined by MacLaurin series, Chelsea Publ. Comp., New York, (1960). Google Scholar

[2] 2. Gawronski, W., Asymptotic distribution of the zeros of power series, Serd. Bulg. math. publ. vol. 5, 13. 23 (1979). Google Scholar

[3] 3. Gawronski, W. and Peyerimhoff, A., On the zeros of power series with rational coefficients, Arch. Math., 29, 173. 186 (1977). Google Scholar

[4] 4. Gawronski, W., On the zeros of power series with rational coefficients II, Arch. Math., 31, 346. 355 (1978). Google Scholar

[5] 5. Gawronski, W., On the zeros of power series with rational coefficients HI, Arch. Math., 32, 368. 376 (1979). Google Scholar

[6] 6. Gawronski, W., A lower bound for the number of negative zeros of power series, Canad. Math. Bull., vol. 22 (1), 47. 52 (1979). Google Scholar

[7] 7. Jurkat, W. B. and Peyerimhoff, A., On power series with negative zeros, Tôhoku Math. J., vol. 24, no. 2, 207. 221 (1972). Google Scholar

[8] 8. Olver, F., Introduction to asymptotics and special functions, Academic Press, Inc., New York, London, (1974). Google Scholar

[9] 9. Peyerimhoff, A., On the zeros of power series, Mich. Math. J., vol. 13, 193. 214 (1966). Google Scholar

[10] 10. Pôlya, G. and Szegô, G., Aufgaben und Lehrsâtze aus der Analysis I, II, Springer-Verlag, Berlin, Heidelberg, New York, (1970). Google Scholar

[11] 11. Sansone, G. and Gerretsen, J., Lectures on the theory of functions of a complex variable, vol. I, P. Noordhoff, Groningen, (1960). Google Scholar

[12] 12. Stadtmuller, U., On the zeros of power series with logarithmic coefficients, Canad. Math. Bull., vol. 22 (2), 221. 233 (1979). Google Scholar

Cité par Sources :