Open AccessOn the convergence of certain integrals
Author(s) -
Mohamed Amine Hachani
Publication year - 2019
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2019.73.1.19-25
Subject(s) - beta (programming language) , combinatorics , mathematics , convergence (economics) , function (biology) , alpha (finance) , beta function (physics) , physics , statistics , quantum mechanics , computer science , construct validity , evolutionary biology , economics , biology , programming language , psychometrics , economic growth , quantum gravity , relationship between string theory and quantum field theory , quantum
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.