Irrational bounds for quotients of Whittaker functions of the first and second kind

Assefa, Genet; Baricz, Árpád

doi:10.1090/proc/17263

Irrational bounds for quotients of Whittaker functions of the first and second kind
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by Genet M. Assefa and Árpád Baricz;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/17263

Published electronically: April 14, 2025

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Abstract:

In this paper, some new sharp inequalities are obtained for ratios of Whittaker functions of the first and second kind by using the first order difference-differential equations satisfied by these functions. Moreover, by using the ideas of Segura, it is shown how to generate iteratively lower and upper bounds for ratios of Whittaker functions of the first and second kind as well as for their logarithmic derivative. The results of the paper extend some of the known results on modified Bessel functions of the first and second kind and are based on the qualitative behaviour of solutions of the Riccati equations satisfied by the ratios of Whittaker functions of the first and second kind.

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Irrational bounds for quotients of Whittaker functions of the first and second kind
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Abstract: