The Univalent Function Created by the Meromorphic Functions Where Defined on the Period Lattice
Abstract
The function $ \xi(z)$ is obtained from the logarithmic derivative function $\sigma(z)$. The elliptic function $ \wp(z) $ is also derived from the $ \xi(z) $ function. The function $ \wp(z) $ is a function of double periodic and meromorphic function on lattices region. The function $ \wp(z) $ is also double function. The function $ \varphi(z) $ meromorphic and univalent function was obtained by the serial expansion of the function $ \wp(z)$. The function $ \varphi(z) $ obtained here is shown to be a convex function.
Keywords
Convex function,Elliptic function,Latices,Meromorphic function
References
- [1] M. Dutta, L. Debnath, Elements of the Elliptic and Associated Functions with Application, Calcutta, 1965.
- [2] A. W. Goodman, Univalent Functions, Florida, 1983.
- [3] P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
