2017/01/29 by Árpád Baricz, Baricz, Árpád, Khaled Mehrez +1
Mathematics · #Mathematical Inequalities and Applications #Analytic and geometric function theory #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.1701.08446
In this paper our aim is to show some new inequalities of Redheffer type for\nBessel and modified Bessel functions of the first kind. The key tools in our\nproofs are some classical results on the monotonicity of quotients of\ndifferentiable functions as well as on the monotonicity of quotients of two\npower series. We use also some known results on the quotients of Bessel and\nmodified Bessel functions of the first kind, and by using the monotonicity of\nthe Dirichlet eta function we prove a sharp inequality for the tangent\nfunction. At the end of the paper a conjecture is stated, which may be of\ninterest for further research.\n