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Brannan's conjecture and trigonometric sums


Authors: Roger W. Barnard, Udaya C. Jayatilake and Alexander Yu. Solynin
Journal: Proc. Amer. Math. Soc. 143 (2015), 2117-2128
MSC (2010): Primary 30C10, 30C50
DOI: https://doi.org/10.1090/S0002-9939-2015-12398-2
Published electronically: January 22, 2015
MathSciNet review: 3314120
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Abstract: We prove some versions of Brannan's Conjecture on Taylor coefficients of the ratio of two binomials of the form $ (1+zx)^\alpha /(1-x)^\beta $ and discuss some related inequalities for trigonometric sums.


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Additional Information

Roger W. Barnard
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: roger.w.barnard@ttu.edu

Udaya C. Jayatilake
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
Address at time of publication: Department of Mathematics, Faculty of Engineering, University of Moratuwa, Katubedda, Moratuwa, Sri Lanka
Email: ucjaya@uom.lk

Alexander Yu. Solynin
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
Email: alex.solynin@ttu.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12398-2
Keywords: Brannan's conjecture, trigonometric sums
Received by editor(s): July 19, 2013
Received by editor(s) in revised form: November 3, 2013
Published electronically: January 22, 2015
Additional Notes: The research of the third author was partially supported by NSF grant DMS-1001882
Communicated by: Jeremy T. Tyson
Article copyright: © Copyright 2015 American Mathematical Society