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  2. Elementary function - Wikipedia

    en.wikipedia.org/wiki/Elementary_function

    In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).

  3. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    1.5 Inequalities. 2 Polynomials and ... Download as PDF; Printable version; ... This is a list of limits for common functions such as elementary functions. In this ...

  4. Elliptic integral - Wikipedia

    en.wikipedia.org/wiki/Elliptic_integral

    Download as PDF; Printable version ... be expressed in terms of elementary functions. ... be in an imaginary quadratic field [note 1] is sufficient. [4] [5] ...

  5. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    Given its domain and its codomain, a function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. [note 1] [4] When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.

  6. László Kalmár - Wikipedia

    en.wikipedia.org/wiki/László_Kalmár

    Kalmar defined what are known as elementary functions, number-theoretic functions (i.e. those based on the natural numbers) built up from the notions of composition and variables, the constants 0 and 1, repeated addition + of the constants, proper subtraction ∸, bounded summation and bounded product (Kleene 1952:526).

  7. Liouville's theorem (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Liouville's_theorem...

    Thus, on an intuitive level, the theorem states that the only elementary antiderivatives are the "simple" functions plus a finite number of logarithms of "simple" functions. A proof of Liouville's theorem can be found in section 12.4 of Geddes, et al. [4] See Lützen's scientific bibliography for a sketch of Liouville's original proof [5 ...

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  9. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Dirac delta function: everywhere zero except for x = 0; total integral is 1. Not a function but a distribution, but sometimes informally referred to as a function, particularly by physicists and engineers. Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous.

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