Bounds and Turán type inequalities for Ferrers functions of the first kind

Abstract

In this paper we investigate the monotonicity properties of the ratio of Ferrers functions of the first kind and we use these properties to derive functional bounds for this ratio, which are shown to be sharp and asymptotically accurate for large values of the parameters. By using these bounds, we establish the convexity of the Ferrers function of the first kind and we obtain some Turán type inequalities with respect to both of the parameters, which are sharp at the endpoints of the argument. Finally, we propose some open problems concerning the log-convexity and log-concavity of Ferrers functions of the first kind. © 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.