Carlson and Shaffer [B.C. Carlson, D.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984) 737–745] have introduced a linear operator associated with the Gaussian hypergeometric function which has been generalized by Dziok and Srivastava [J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl....

In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation transform into system, where extinction steady state is represented by up three distinct states, whose existence determined values of appropriate Lambert W functions. We in...

We show that there exists a rational change of coordinates of Painlev e's P1 equation y 00 = 6y 2 +x and of the elliptic equation y 00 = 6y 2 after which these two equations become analytically equivalent in a region in the complex phase space where y and y 0 are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solution...

This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. This article is an exposition for non-specialists of Ahlfors’ work in the theory of meromorphic functions. When the domain is not specified we mean meromorphic functions in the complex plane C. The theory of meromorphic functions probably begins with t...

Given a point p ∈ C and a real number r > 0 we denote by B2n(p, r) the open ball of radius r centered at p in C. The corresponding closed ball is denoted by B2n[p, r] and its boundary sphere by S2n−1(p, r) = ∂B2n[p, r]. We also write B2n(1) = B2n(0, 1), B2n[1] = B2n[0, 1] and S2n−1(1) = ∂B2n[1]. Let Ω be a germ of holomorphic one-form with an isolated singularity at the origin 0 ∈ C, n ≥ 3. We ...