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  2. Symmetric function - Wikipedia

    en.wikipedia.org/wiki/Symmetric_function

    Aside from polynomial functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric -tensors on a vector space is isomorphic to the space of homogeneous polynomials of degree on . Symmetric functions should not be confused with even and odd functions, which have a different sort of symmetry.

  3. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin. Examples of odd functions are x, x 3, sin(x), sinh(x), and erf(x).

  4. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    A function's being odd or even does not imply differentiability, or even continuity. For example, the Dirichlet function is even, but is nowhere continuous. In the following, properties involving derivatives, Fourier series, Taylor series are considered, and these concepts are thus supposed to be defined for the considered functions.

  5. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    Examples include even and odd functions in calculus, symmetric groups in abstract algebra, symmetric matrices in linear algebra, and Galois groups in Galois theory. In statistics, symmetry also manifests as symmetric probability distributions, and as skewness—the asymmetry of distributions. [16]

  6. Dirac delta function - Wikipedia

    en.wikipedia.org/wiki/Dirac_delta_function

    In particular, the delta function is an even distribution (symmetry), in the sense that ... For example, the probability density function f(x) ...

  7. Symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Symmetric_polynomial

    One context in which symmetric polynomial functions occur is in the study of monic univariate polynomials of degree n having n roots in a given field.These n roots determine the polynomial, and when they are considered as independent variables, the coefficients of the polynomial are symmetric polynomial functions of the roots.

  8. Beta function - Wikipedia

    en.wikipedia.org/wiki/Beta_function

    When m (or n, by symmetry) is a positive integer, ... In Microsoft Excel, for example, the complete beta function can be computed with the GammaLn function ...

  9. Ring of symmetric functions - Wikipedia

    en.wikipedia.org/wiki/Ring_of_symmetric_functions

    The following are fundamental examples of symmetric functions. The monomial symmetric functions m α. Suppose α = (α 1,α 2,...) is a sequence of non-negative integers, only finitely many of which are non-zero. Then we can consider the monomial defined by α: X α = X 1 α 1 X 2 α 2 X 3 α 3....

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