On the convergence of certain integrals

Mohamed Amine Hachani

Abstract


Let \(M(r) := \max_{|z|=r} |f(z)|\), where \(f(z)\) is an entire function. Also let \(\alpha> 0\) and \(\beta>1\). We discuss the behavior of the integrand \(M(r)e^{-\alpha(log r)^\beta}\) as \(r \to \infty\) if \(\int_1^\infty M(r)e^{-\alpha(log r)^\beta}dr\) is convergent.

Keywords


Entire functions; Hadamard’s three-circles theorem; infinite integrals

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References


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DOI: http://dx.doi.org/10.17951/a.2019.73.1.19-25
Date of publication: 2019-12-19 10:33:45
Date of submission: 2019-12-17 09:41:01


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