section_path: Trigonometric functions of real or complex variables/Power series representations
section_name: Power series representations
paragraph_text: Power series representations
  
  When considered as functions of a real variable, the trigonometric ratios can be represented by an infinite series. For instance, sine and cosine have the following representations:
  
  With these definitions the trigonometric functions can be defined for complex numbers. When extended as functions of real or complex variables, the following formula holds for the complex exponential:
  
  This complex exponential function, written in terms of trigonometric functions, is particularly useful.