Transcendental function

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.[1][2]

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

  1. ^ Townsend, E.J. (1915). Functions of a Complex Variable. H. Holt. p. 300. OCLC 608083625.
  2. ^ Hazewinkel, Michiel (1993). Encyclopedia of Mathematics. Vol. 9. pp. 236.