On the elliptic function obtained from the theta function and dedekind's eta function

It's a reality that there is a relationship between the sigma function of Weierstrass and theta functions. An elliptic function can be set up using the theta functions just as it can be established with the help of sigma function of Weierstrass and two relations between the Dedekind's ?-function and ?-theta function were established by the using characteristic values for ?-function according to the (z,?) pair and z,? complex numbers, satisfying Im?>0. This thesis consists of three sections. In the first section, a short literature survey is given. The definitions and basic theorems which used for this study are provided in this section.. In the second section, firstly periodic functions, elliptic functions, Weierstrass functions, theta functions, Jacobi elliptic functions and Dedekind eta function are defined and then some relations between them are given. In the third section, the transformations among the theta functions according to the quarter periods have been given and a Jacobian style elliptic functions has been set up the theta function by the help of a defined function.