Redheffer type bounds for Bessel and modified Bessel functions of the first kind
In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.
KeywordsBessel and modified Bessel functions of the first and second kind Zeros of Bessel functions Redheffer type inequalities Rayleigh sum of zeros of Bessel functions of the first kind
Mathematics Subject Classification33C10
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