On the Elliptic Function Arising from the Theta Functions and Dedekind's η-Function
Ismet Yildiz and Neslihan Uyanik
DOI : 10.3844/jmssp.2005.153.159
Journal of Mathematics and Statistics
Volume 1, Issue 2
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 astablished with the help of sigma function of Weierstrass and two relations between the Dedekind's h-function and - theta function were established by the using characteristic values (mod2) for θ-function according to the (u,τ) pair and u,τ complex numbers, satisfying Im τ>0. In this study, 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.
© 2005 Ismet Yildiz and Neslihan Uyanik. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.