What makes a function transcendental?

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- March 19th 2014, 03:10 PMnycmathTranscendental Functions
What makes a function transcendental?

- March 19th 2014, 04:39 PMromsekRe: Transcendental Functions
- March 19th 2014, 05:02 PMnycmathRe: Transcendental Functions
romsek,

I could also do research on this function. I want an easy definition and explanation not the technical, textbook version. - March 19th 2014, 06:06 PMromsekRe: 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. - March 19th 2014, 06:14 PMnycmathRe: Transcendental Functions
- March 19th 2014, 06:20 PMromsekRe: 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. - March 19th 2014, 06:21 PMnycmathRe: Transcendental Functions
Great. Look for one or two more integral questions tomorrow.