کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6418634 | 1339345 | 2013 | 11 صفحه PDF | دانلود رایگان |
We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form Gα,β(t)=t/(α+t2+β2) in case Rν is positive for all t>0, or equivalently, where νâ¥â1 or ν is a negative integer. For νâ¥â1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If νâ¥â1/2, the minimal elements are tangent to Rν in exactly one point 0â¤tâ¤â, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.
Journal: Journal of Mathematical Analysis and Applications - Volume 408, Issue 1, 1 December 2013, Pages 91-101