Geodesic
On the convergence of certain integrals
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1.

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Let M(r) := max_|z|=r |f(z)|, where f(z) is an entire function. Also let α> 0 and β>1. We discuss the behavior of the integrand M(r)e^-α(log r)^β as r →∞ if ∫_1^∞ M(r)e^-α(log r)^βdr is convergent.
Keywords: Entire functions, Hadamard’s three-circles theorem, infinite integrals 
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Hachani, Mohamed Amine. On the convergence of certain integrals. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1. http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a5/

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