# Transcendental Functions

• Mar 19th 2014, 03:10 PM
nycmath
Transcendental Functions
What makes a function transcendental?
• Mar 19th 2014, 04:39 PM
romsek
Re: Transcendental Functions
• Mar 19th 2014, 05:02 PM
nycmath
Re: Transcendental Functions
romsek,

I could also do research on this function. I want an easy definition and explanation not the technical, textbook version.
• Mar 19th 2014, 06:06 PM
romsek
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.
• Mar 19th 2014, 06:14 PM
nycmath
Re: Transcendental Functions
Quote:

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?
• Mar 19th 2014, 06:20 PM
romsek
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.
• Mar 19th 2014, 06:21 PM
nycmath
Re: Transcendental Functions
Great. Look for one or two more integral questions tomorrow.