Exponential bounds for the logarithmic derivative of Whittaker functions
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- by Genet M. Assefa and Árpád Baricz;
- Proc. Amer. Math. Soc. 151 (2023), 4867-4880
- DOI: https://doi.org/10.1090/proc/16549
- Published electronically: August 4, 2023
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Abstract:
Some well-known results of Grönwall on logarithmic derivative of modified Bessel functions of the first kind concerning exponential bounds are extended to Whittaker functions of the first and second kind $M_{\kappa ,\mu }$ and $W_{\kappa ,\mu }$. Moreover, a complete monotonicity result is proved for the logarithmic derivative of the Whittaker function $W_{\kappa ,\mu },$ and some monotonicity results with respect to the parameters and argument are shown for the logarithmic derivative of $M_{\kappa ,\mu }.$ The results extend and complement the known results in the literature about modified Bessel functions of the first and second kind.References
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Bibliographic Information
- Genet M. Assefa
- Affiliation: Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
- Email: genetmekonnen428@gmail.com
- Árpád Baricz
- Affiliation: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania; and Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
- MR Author ID: 729952
- Email: bariczocsi@yahoo.com
- Received by editor(s): February 2, 2023
- Received by editor(s) in revised form: April 27, 2023
- Published electronically: August 4, 2023
- Additional Notes: The second author is the corresponding author.
- Communicated by: Mourad Ismail
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4867-4880
- MSC (2020): Primary 33C15; Secondary 30C10
- DOI: https://doi.org/10.1090/proc/16549
- MathSciNet review: 4634889
Dedicated: Á. Baricz dedicates this paper to his wife Katinka