Abstract
We establish inequalities for the Bessel functions Jν (x) of the first kind, by means of the arithmetic geometric mean inequality and the Infinite product formula for Jν(x). A concavity property is also obtained for the positive zeros jνk(k = 1, 2, …) of Jν(x) using a lower bound for the second derivative of recently established in [3]. Finally we show a monotonicity property of the zeros of Legendre polynomials. This property is proved as a consequence of the classical Sturm comparison theorem.
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© 1987 Birkhäuser Verlag Basel
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Giordano, C., Laforgia, A. (1987). Inequalities for Some Special Functions and their Zeros. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_11
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DOI: https://doi.org/10.1007/978-3-0348-7192-1_11
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