Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Some monotonicity results for ratios of modified Bessel functions

Authors: Henry C. Simpson and Scott J. Spector
Journal: Quart. Appl. Math. 42 (1984), 95-98
MSC: Primary 33A40; Secondary 73G05
DOI: https://doi.org/10.1090/qam/736509
MathSciNet review: 736509
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Abstract: We consider the functions $ {v_\alpha }(t) \equiv t{I_\alpha }(t)/{I_{\alpha + 1}}(t)$ where $ {I_\alpha }$ are the modified Bessel functions of the first kind of order $ \alpha \ge 0$. We prove that $ {v_\alpha }$ is strictly monotone and strictly convex on R$ ^{+}$ . These results have application in finite elasticity$ ^{1}$.

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DOI: https://doi.org/10.1090/qam/736509
Article copyright: © Copyright 1984 American Mathematical Society

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