Analytic representation of the generalized Pascal snail and its applications

Abstract

We find an unifying approach to the analytic representation of the domain bounded by a generalized Pascal snail. Special cases as Pascal snail, Both leminiscate, conchoid of the Sluze and a disc are included. The behavior of functions related to generalized Pascal snail are demonstrated.1991 Mathematics Subject Classification. 30C80, 30C45. Key words and phrases. domain bounded by the generalized Pascal snail, Booth leminiscate, conchoid of the Sluze, Pascal snail, univalent functions, applied mathematics, starlike and convex functions.