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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Higher monotonicity properties and inequalities for zeros of Bessel functions


Authors: Laura Nicolò-Amati Gori, Andrea Laforgia and Martin E. Muldoon
Journal: Proc. Amer. Math. Soc. 112 (1991), 513-520
MSC: Primary 33C10
MathSciNet review: 1062389
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Abstract: L. Lorch and P. Szegö have considered the sign-regularity of the higher differences (with respect to the rank $ k$) of the sequence $ \{ {c_{\nu k}}\} $ of positive zeros of the Bessel function $ {C_\nu }(x)$. Our main purpose here is to extend one of their main results to the higher derivatives with respect to $ \kappa $ when $ {c_{\nu k}}$ is appropriately defined as a function of a continuous variable $ \kappa $ rather than the discrete variable $ k$, and the difference operator is replaced by a derivative operator. We also present some inequalities arising from these and other results.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062389-7
PII: S 0002-9939(1991)1062389-7
Keywords: Bessel functions, zeros, higher monotonicity, inequalities
Article copyright: © Copyright 1991 American Mathematical Society