transcendental

(adjective)

of or relating to a number that is not the root of any polynomial that has positive degree and rational coefficients

Related Terms

  • irrational

Examples of transcendental in the following topics:

  • Further Transcendental Functions

    • A transcendental function is a function that is not algebraic.
    • Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions.
    • Formally, an analytic function $ƒ(z)$ of the real or complex variables $z_1, \cdots ,z_n$ is transcendental if $z_1, \cdots ,z_n$, $ƒ(z)$ are algebraically independent, i.e., if $ƒ$ is transcendental over the field $C(z_1, \cdots ,z_n)$.
    • Because of this, transcendental functions can be an easy-to-spot source of dimensional errors.
    • Identify a transcendental function as one that cannot be expressed as the finite sequence of an algebraic operation
  • The Natural Logarithmic Function: Differentiation and Integration

    • The natural logarithm, generally written as $\ln(x)$, is the logarithm with the base e, where e is an irrational and transcendental constant approximately equal to $2.718281828$.
  • Real Numbers, Functions, and Graphs

    • The real numbers include all the rational numbers, such as the integer -5 and the fraction $\displaystyle \frac{4}{3}$, and all the irrational numbers such as $\sqrt{2}$ (1.41421356… the square root of two, an irrational algebraic number) and $\pi$ (3.14159265…, a transcendental number).
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