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math.CA2026
Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative
Javier Segura, Soichiro Suzuki
We prove that, for all , the product of modified Bessel functions satisfies \[ \frac{1}{2\sqrt{x^2+ν^2+1/5}}<I_ν(x)K_ν(x)<\frac{1}{2\sqrt{x^2+ν^2-1/4}} , \] where the lower…
math.CA2026
Optimized bounds for the product and the ratios of modified Bessel functions
Javier Segura, Soichiro Suzuki
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…