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Math Help - Transcendental Functions

  1. #1
    Senior Member nycmath's Avatar
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    Transcendental Functions

    What makes a function transcendental?
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    Senior Member nycmath's Avatar
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    Re: Transcendental Functions

    romsek,

    I could also do research on this function. I want an easy definition and explanation not the technical, textbook version.
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    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.
    Last edited by romsek; March 19th 2014 at 06:18 PM.
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    Senior Member nycmath's Avatar
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    Re: Transcendental Functions

    Quote Originally Posted by romsek View Post
    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?
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    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.
    Last edited by romsek; March 19th 2014 at 06:22 PM.
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    Senior Member nycmath's Avatar
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    Re: Transcendental Functions

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