贝塞尔函数
数学
斯图鲁弗函数
贝塞尔多项式
贝塞尔过程
产品(数学)
圆柱谐波
类型(生物学)
零(语言学)
数学证明
无穷
纯数学
商
数学分析
域代数上的
正交多项式
几何学
差分多项式
生物
Gegenbauer多项式
语言学
经典正交多项式
生态学
哲学
麦克唐纳多项式
标识
DOI:10.1016/j.exmath.2014.07.001
摘要
Motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences, new tight Turán type inequalities for modified Bessel functions of the first and second kind are deduced. These inequalities provide sharp lower and upper bounds for the Turánian of modified Bessel functions of the first and second kind, and in most cases the relative errors of the bounds tend to zero as the argument tends to infinity. The chief tools in our proofs are some ideas of Gronwall [19] on ordinary differential equations, an integral representation of Ismail [28,29] for the quotient of modified Bessel functions of the second kind and some results of Hartman and Watson [24,26,59]. As applications of the main results some sharp Turán type inequalities are presented for the product of modified Bessel functions of the first and second kind and it is shown that this product is strictly geometrically concave.
科研通智能强力驱动
Strongly Powered by AbleSci AI