Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)
- Volume: 70, Issue: 1
- ISSN: 0365-1029
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topM. A. Qazi. "Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.1 (2016): null. <http://eudml.org/doc/289801>.
@article{M2016,
abstract = {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.},
author = {M. A. Qazi},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Entire functions; Hadamard's three circles theorem; Euler's Gamma function},
language = {eng},
number = {1},
pages = {null},
title = {Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem},
url = {http://eudml.org/doc/289801},
volume = {70},
year = {2016},
}
TY - JOUR
AU - M. A. Qazi
TI - Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 1
SP - null
AB - 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.
LA - eng
KW - Entire functions; Hadamard's three circles theorem; Euler's Gamma function
UR - http://eudml.org/doc/289801
ER -
References
top- Boas, Jr., R. P., Entire Functions, Academic Press, New York, 1954.
- Boas, Jr., R. P., A Primer of Real Functions, The Carus mathematical monographs, No. 13, The Mathematical Association of America, 1960.
- Hardy, G. H., The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14 (1915), 269-277.
- Henrici, P., Applied and Computational Complex Analysis, Vol. 2, (A Wiley-
- Interscience publication), John Wiley & Sons, New York, 1977.
- Rahman, Q. I., Interpolation of Entire functions, Amer. J. Math. 87 (1965), 1029-1076.
- Titchmarsh, E. C., The Theory of Functions, 2nd ed. Oxford University Press, 1939.
- Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, New York, 1949.
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