On the convergence of certain integrals

• Autorzy: Mohamed Amine Hachani
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2019
• Tom: 73
• Numer: 1

Daty

wydano

2019

online

2019-12-19

Twórcy

autor

Mohamed Amine Hachani

Bibliografia

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• Qazi, M. A., Application of the Euler’s gamma function to a problem related to F. Carlson’s uniqueness theorem, Ann. Univ. Mariae Curie-Skłodowska Sect. A 70 (1) (2016), 75–80.
• Rahman, Q. I., On means of entire functions, Q. J. Math. 7 (1) (1956), 192–195.
• Rahman, Q. I., Interpolation of entire functions, Amer. J. Math. 87 (1965), 1029–1076.
• Titchmarsh, E. C., The Theory of Functions, 2nd Edition, Oxford University Press, London, 1939.
• Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, New York, 1949.

Identyfikatory

DOI

10.17951/a.2019.73.1.19-25