transcendental function

English

Noun

transcendental function (plural transcendental functions)

1. (mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.

   An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.

2. (specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function.

Further reading

• Transcendental function on Wikipedia.Wikipedia
• Transcendental function on Encyclopedia of Mathematics
• Transcendental Function on Wolfram MathWorld