New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean - Ling Zhu (Mathematics, 2021)
Let <semantics>Ip<mfenced open="(" close=")">x</mfenced></semantics> be the modified Bessel function of the first kind of order p. The upper and lower bounds in the form of simple rational functions about <semantics>cosht</semantics> and <semantics>(sinht)/t</semantics> for the function <semantics>I0<mfenced open="(" close=")">x</mfenced></semantics> are obtained. The corresponding inequalities for the Toader-Qi mean do not match those in the existing literature.