On generalized trigonometric functions and series of rational functions

Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials. The well known trigonometric functions can be seen to be associated with polynomial x2−1. We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin2⁡(x)+cos2⁡(x)=1. One application of the generalized trigonometric functions is in evaluating infinite series of rational functions.