Editing Transcendental function (section)

{{Short description|Analytic function that does not satisfy a polynomial equation}}

In [[mathematics]], a '''transcendental function''' is an [[analytic function]] that does not satisfy a [[polynomial]] equation whose coefficients are functions of the independent variable that can be written using only the basic operations of addition, subtraction, multiplication, and division (without the need of taking limits). This is in contrast to an [[algebraic function]].<ref>{{cite book |first=E.J. |last=Townsend |title=Functions of a Complex Variable |publisher=H. Holt |location= |date=1915 |oclc=608083625 |pages=300 |url=}}</ref><ref>{{cite book |first=Michiel |last=Hazewinkel |title=Encyclopedia of Mathematics |publisher= |volume=9 |date=1993 |isbn= |pages=[https://books.google.com/books?id=1ttmCRCerVUC&pg=PA236 236] |url=}}</ref> 

Examples of transcendental functions include the [[exponential function]], the [[logarithm]] function, the [[hyperbolic function]]s, and the [[trigonometric function]]s. Equations over these expressions are called [[transcendental equation]]s.