Geodesic
On a functional equation for the exponential function of a complex variable
Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 31-34

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

The following result is well known in the theory of analytic functions; see [1].Theorem A. Suppose that f(z) is an entire function of a complex variable z. Then f(z) satisfies the functional equationwhere z = x + iy (x, y real), if and only if f(z) = aexp(sz), where a is an arbitrary complex constant and s is an arbitrary real constant. 
Haruki, Hiroshi. On a functional equation for the exponential function of a complex variable. Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 31-34. doi: 10.1017/S0017089500001117
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[1] 1.Hille, E., A class of functional equations, Ann. of Math. 29 (1928), 215–222. Google Scholar | DOI

[2] 2.Nevanlinna, R. und Polya, G., Unitare Transformationen analytischer Funktionen, Jber. Deutsch. Math. -Verein. 40 (1931), 80 (Aufgabe 103). Google Scholar

[3] 3.Pólya, G. und Szego, G., Aufgaben und Lehrsatze aus der Analysis I, p. 94. Berlin-Gottingen-Heidelberg, Springer Verlag, 1954. Google Scholar | DOI

[4] 4.Schmidt, H., Losung der Aufgabe 103, Jber. Deutsch. Math. -Verein. 43 (1934), 6–7. Google Scholar

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