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Zbl 0952.33002
Pal'tsev, B.V.
Two-sided bounds uniform in the real argument and the index for modified Bessel functions. (English. Russian original)
[J] Math. Notes 65, No.5, 571-581 (1999); translation from Mat. Zametki 65, No.5, 681-692 (1999). ISSN 0001-4346; ISSN 1573-8876/e

Two-sided bounds are derived for the modified Bessel functions and the functions $a_\nu(x)=xI_\nu'(x)/I_\nu(x)$ and $b_\nu(x)=xK_\nu'(x)/K_\nu(x)$ for $x>0$, $\nu\ge 0$, except for some neighborhoods of the point $(x,\nu)=(0,0)$. The bounds are obtained by using the Riccati equation for $a_\nu(x)$, $b_\nu(x)$, and a general theorem on inequalities for solutions of a type of differential equations.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33C10 Cylinder functions, etc.
34C11 Qualitative theory of solutions of ODE: Growth, etc.
26D07 Inequalities involving other types of real functions
26D10 Inequalities involving derivatives, diff. and integral operators

Keywords: Bessel functions; modified Bessel functions; inequalities; differential inequality

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