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Two-sided bounds uniform in the real argument and the index for modified Bessel functions. (English) Zbl 0952.33002
Two-sided bounds are derived for the modified Bessel functions and the functions a ν (x)=xI ν ' (x)/I ν (x) and b ν (x)=xK ν ' (x)/K ν (x) for x>0, ν0, except for some neighborhoods of the point (x,ν)=(0,0). The bounds are obtained by using the Riccati equation for a ν (x), b ν (x), and a general theorem on inequalities for solutions of a type of differential equations.
MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
34C11Qualitative theory of solutions of ODE: growth, boundedness
26D07Inequalities involving other types of real functions
26D10Inequalities involving derivatives, differential and integral operators
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