Zeros of Bessel functions: monotonicity, concavity, inequalities

Abstract

We present a survey of the most important inequalities and monotonicity, concavity (convexity) results of the zeros of Bessel functions. The results refer to the definition Jνκ of the zeros of Cν (x) = Jν (x) cosα −Yν (x) sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results.

Keywords

• Sturm comparison theorem
• Zeros of Bessel functions
• Inequalities
• Monotonicity
• Concavity (convexity) properties
• Watson formula