On generalized trigonometric functions and series of rational functions

摘要

Abstract 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 x 2 ? 1 . We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin 2 ? ( x ) + cos 2 ? ( x ) = 1 . One application of the generalized trigonometric functions is in evaluating infinite series of rational functions. ]]>