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Optimized bounds for the product and the ratios of modified Bessel functions
New sharp bounds for the product and the ratios of modified Bessel functions are presented. Most bounds for the product are derived as direct consequences of previously established bounds for the ratios of consecutive orders, except for the lower bound $I_ν(x)K_ν(x) > \frac{1}{2}(x^2 + ν^2 + 1/5)^{-
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