Sharp Becker-Stark-Type Inequalities for Bessel Functions
© Ling Zhu. 2010
Received: 22 January 2010
Accepted: 23 March 2010
Published: 6 April 2010
We extend the Becker-Stark-type inequalities to the ratio of two normalized Bessel functions of the first kind by using Kishore formula and Rayleigh inequality.
In recent paper , we obtained the following further result.
Moreover, the following refinement of the Becker-Stark inequality was established in .
Particularly for and , respectively, the function reduces to some elementary functions, like [4, page 54] and . In view of that , in Section 3 we shall extend the result of Theorem 1.3 to the ratio of two normalized Bessel functions of the first kind and .
2. Some Lemmas
In order to prove our main result in next section, each of the following lemmas will be needed.
where , and is the Rayleigh function of order , which showed in [4, page 502].
3. Main Result and Its Proof
Proof of Theorem 3.1.
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