Delange's characterization of the sine function
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 66-68
Voir la notice de l'article provenant de la source Cambridge University Press
In [2], H. Delange gives the following characterization of the sine function.Theorem A. f(x)=sin x is the only infinitely differentiable real-valued function on the real line such that f'(O)= 1 andfor all real x and n = 0,1,2,....It is clear that, if f satisfies (1), then the analytic continuation of f is an entire function satisfyingfor all z in the complex plane. Hence f is of at most order one and type one. In this note, we prove the following theorem.
Ching, Chin-Hung; Chui, Charles K. Delange's characterization of the sine function. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 66-68. doi: 10.1017/S0017089500002147
@article{10_1017_S0017089500002147,
author = {Ching, Chin-Hung and Chui, Charles K.},
title = {Delange's characterization of the sine function},
journal = {Glasgow mathematical journal},
pages = {66--68},
year = {1974},
volume = {15},
number = {1},
doi = {10.1017/S0017089500002147},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002147/}
}
TY - JOUR AU - Ching, Chin-Hung AU - Chui, Charles K. TI - Delange's characterization of the sine function JO - Glasgow mathematical journal PY - 1974 SP - 66 EP - 68 VL - 15 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002147/ DO - 10.1017/S0017089500002147 ID - 10_1017_S0017089500002147 ER -
[1] 1.Boas, R. P., Entire Functions (New York, 1954). Google Scholar
[2] 2.Delange, H., Caractérisations des fonctions circulaires, Bull. Sc. Math. 91 (1967), 65–73. Google Scholar
[3] 3.Duffin, R. J. and Schaeffer, A. C., On the extension of a functional inequality of S. Bernstein to non-analytic functions, Bull. Amer. Math. Soc. 46 (1940), 356–363. Google Scholar | DOI
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