Volume : 3, Issue : 4, April - 2014

Elliptic Functions With A View Toward Jacobi Hyperbolic Functions

Ms. Parveen Bawa

Abstract :

In Complex Analysis an elliptic function is a doubly periodic meromorphic function which is determined by its value on a fundamental parallelogram which then repeat in a lattice. Elliptic functions must have at least two poles in a fundamental parallelogram.  Jacobi elliptic functions can be expressed in various forms namely as a Trigonometric functions, Theta functions, as a solution of first and second order differential equations etc. In the present paper a new concept of Jacobi Hyperbolic functions using Hyperbola is being developed. Jacobi Hyperbolic functions are related to elliptic functions with complex arguments, just as hyperbolic sines and cosines functions are related to sines and cosines of complex argument. Just like Jacobi elliptic functions, Jacobi Hyperbolic functions are meromorphic functions that are periodic in two directions and can also be represented in various other functions. In the present study Jacobi Hyperbolic functions are being presented in the form of Trigonometric functions, which are also used as the solutions of first and second order differential equations.