On a simultaneous characterization of the poisson law and the gamma distribution
The authors consider the following problem due to A Rényi and I Vincze: if for the entire function f(t)=1+a1t+a2t2+. ... with positive coefficients we have Open image in new window then is it necessary that f(t) ≡ et? Some results in this direction were proved in , . Now it is shown that if 1/f is completely monotone then we must have f(t) ≡ et.
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- Hayman, W.K. and Vincze, I., A problem on entire functions, Complex Analysis and its Applications, dedicated to I.N. Vekua on his 70th birthday. Izd. Nauka, Moskow 1978, 191–194.Google Scholar