Sharp Jordan-type inequalities for Bessel functions

• Autores: Arpád Baricz, Shanhe Wu
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 74, Fasc. 1-2, 2009, págs. 107-126
• Idioma: inglés
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• Resumen

  • In this paper our aim is to establish some sharp Jordan and Kober type inequali- ties for Bessel and modi¯ed Bessel functions of the ¯rst kind by using the monotone form of l'Hospital's rule. Moreover, by using the classical Cauchy mean value theo- rem inductively we deduce new series expansions for the Bessel and modi¯ed Bessel functions. These results extend and improve many known results in the literature.