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 | References | Similar Articles | Additional Information

Abstract: We consider the functions where are the modified Bessel functions of the first kind of order . We prove that is strictly monotone and strictly convex on **R** . These results have application in finite elasticity.

**[1]**D. E. Amos,*Computation of modified Bessel functions and their ratios*, Math. Comp.**28**, 239-251 (1974) MR**0333287****[2]**S. Y. Cheng, S. T. Ariaratnam and R. N. Dubey,*Axisymmetric bifurcation in an elastic-plastic cylinder under axial load and lateral hydrostatic pressure*, Quart. Appl. Math.**29**, 41-51 (1971)**[3]**J. A. Cochran,*The monotonicity of modified Bessel functions with respect to their order*, J. Math. and Phys.**46**, 220-222 (1967) MR**0213624****[4]**A. E. Green and A. J. M. Spencer,*The stability of a circular cylinder under finite extension and torsion*, J. Math. and Phys.**37**, 316-338 (1959) MR**0101660****[5]**M. E. H. Ismail and D. H. Kelker,*Special functions, Stieltjes transforms and infinite divisibility*, SIAM J. Math. Anal.**10**, 884-901 (1979) MR**541088****[6]**A. L. Jones,*An extension of an inequality involving modified Bessel functions*, J. Math. and Phys.**47**, 220-221 (1968) MR**0227483****[7]**J. P. Miles,*Bifurcation in plastic flow under uniaxial tension*, J. Mech. Phys. Solids**19**, 89-102 (1971)**[8]**I. Nasell,*Inequalities for modified Bessel functions*, Math. Comp.**28**, 253-256 (1974) MR**0333288****[9]**C. B. Sensenig,*Instability of thick elastic solids*. Comm. Pure Appl. Math.**17**, 451-491 (1964) MR**0169453****[10]**H. C. Simpson and S. J. Spector,*On barrelling for a special material in finite elasticity*. Quart. Appl. Math. This issue. MR**736510****[11]**R. P. Soni,*On an inequality for modified Bessel functions*, J. Math. and Phys.**44**, 406-407 (1965) MR**0185164****[12]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Univ. Press (1922) MR**1349110****[13]**E. W. Wilkes,*On the stability of a circular tube under end thrust*, Quart. J. Mech. Appl. Math.**8**, 88-100 (1955) MR**0070415**

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Additional Information

DOI:
https://doi.org/10.1090/qam/736509

Article copyright:
© Copyright 1984
American Mathematical Society