1. ## Transcendental Functions

What makes a function transcendental?

3. ## Re: Transcendental Functions

romsek,

I could also do research on this function. I want an easy definition and explanation not the technical, textbook version.

4. ## Re: Transcendental Functions

mmk

the short way of putting it I guess is that algebraic numbers are the solutions to some polynomial equation with integer coefficients. Rational roots of rational numbers fall into this category as well as rationals, integers, etc.

A transcendental real number is a real number that isn't algebraic.

A transcendental function is one cannot be expressed as a polynomial with algebraic coefficients.

5. ## Re: Transcendental Functions

Originally Posted by romsek
mmk

the short way of putting it I guess is that algebraic numbers are the solutions to some polynomial equation with integer coefficients. Rational roots of rational numbers fall into this category as well as rationals, integers, etc.

A transcendental real number is a real number that isn't algebraic.

A transcendental function is one that can produce a transcendental real number. This is most of the functions you know. All the trig functions, the exponential and log function are transcendental.
What about hyperbolic functions? Are they transcendental, too?

6. ## Re: Transcendental Functions

I updated the definition of these. The one I posted before wasn't really correct. I bet one of the real mathematicians on here can give you a better definition yet.

The hyperbolic trig functions? Yes, these are transcendental. They are made up of exponential functions which are transcendental.

7. ## Re: Transcendental Functions

Great. Look for one or two more integral questions tomorrow.