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Zeros of a cross-product of the Coulomb wave and Tricomi hypergeometric functions


Author: Árpád Baricz
Journal: Proc. Amer. Math. Soc. 145 (2017), 1643-1648
MSC (2010): Primary 34B09, 34B30, 33C15, 33C10
DOI: https://doi.org/10.1090/proc/13331
Published electronically: October 18, 2016
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Abstract: Motivated by a problem on conditions for the existence of clines in genetics, we show that the positive zeros of a cross-product of the regular Coulomb wave function and the Tricomi hypergeometric function are increasing with respect to one of the parameters. In particular, this implies that the eigenvalues of a certain boundary value problem are increasing with the dimension.


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Additional Information

Árpád Baricz
Affiliation: Institute of Applied Mathematics, Óbuda University, Budapest, Hungary – and – Department of Economics, Babeş-Bolyai University, Cluj-Napoca, Romania
Email: bariczocsi@yahoo.com

DOI: https://doi.org/10.1090/proc/13331
Keywords: Coulomb wave function, Tricomi hypergeometric function, boundary value problem, zeros of a cross-product, eigenvalues, eigenfunctions, Bessel and modified Bessel functions, monotonicity of the zeros
Received by editor(s): March 24, 2016
Received by editor(s) in revised form: June 9, 2016
Published electronically: October 18, 2016
Additional Notes: The research of the author was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences
Dedicated: Dedicated to Professor Péter T. Nagy on the occasion of his 70th birthday
Communicated by: Mourad Ismail
Article copyright: © Copyright 2016 American Mathematical Society

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