Monatsh Math (2015) 176:323–330 DOI 10.1007/s00605-014-0708-1 About the radius of starlikeness of Bessel functions of the first kind Róbert Szász Received: 26 September 2013 / Accepted: 11 November 2014 / Published online: 30 December 2014 © Springer-Verlag Wien 2014 Abstract Let J ν denote the Bessel function of the first kind. Brown (Univalence of Bessel functions, pp 278–283, 1960) determined the radius of starlikeness for two kind of normalized Bessel functions in the case ν> 0. We extended these results for ν ∈ (-1, 0) in Baricz et al. (The radius of starlikeness of normalized Bessel functions of the first kind, pp 2019–2025, 2014). Now we deal with the case ν ∈ (-2, -1). The basic idea of the study is the same as in Baricz et al. (The radius of starlikeness of normalized Bessel functions of the first kind, pp 2019–2025, 2014) and Szász (On starlikeness of Bessel functions of the first kind, pp 63–70, 2011), but in this case we have a different situation and a different approach is needed. Keywords Bessel function · Starlike function · Radius of starlikeness Mathematics Subject Classification 33C10 · 30C45 1 Introduction Let r > 0 be a positive number. U (r ) ={z ∈ C :|z | < r } denotes the disk centered at zero and of radius r. Let (a n ) n≥2 be a sequence of complex numbers with L = lim sup n≥2 |a n | 1 n > 0 and let r f = 1 L . Communicated by A. Constantin. R. Szász (B ) Department of Mathematics and Informatics, Faculty of Technical and Human Sciences, Sapientia University, Tg. Mures, Romana e-mail: rszasz@ms.sapientia.ro 123