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Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem

100%

Qazi M. A.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2016

tom 70

nr 1

In his work on F. Carlson's uniqueness theorem for entire functions of exponential type, Q. I. Rahman [5] was led to consider an infinite integral and needed to determine the rate at which the integrand had to go to zero for the integral to converge. He had an estimate for it which he was content with, although it was not the best that could be done. In the present paper we find a result about the behaviour of the integrand at infinity, which is essentially best possible. Stirling's formula for the Euler's Gamma function plays an important role in its proof.

The Schwarz-Pick theorem and its applications

63%

Qazi M. A., Rahman Q. I.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 2

Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.

Ograniczanie wyników

2 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2 Qazi M. A.

1 Rahman Q. I.

1 2016

1 2011

Wyniki wyszukiwania

Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem

The Schwarz-Pick theorem and its applications