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  2. Difference engine - Wikipedia

    en.wikipedia.org/wiki/Difference_engine

    A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was created by Charles Babbage . The name difference engine is derived from the method of finite differences , a way to interpolate or tabulate functions by using a small set of polynomial co-efficients.

  3. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    Every polynomial function is continuous, smooth, and entire. The evaluation of a polynomial is the computation of the corresponding polynomial function; that is, the evaluation consists of substituting a numerical value to each indeterminate and carrying out the indicated multiplications and additions.

  4. Category:Polynomial functions - Wikipedia

    en.wikipedia.org/wiki/Category:Polynomial_functions

    Pages in category "Polynomial functions" The following 14 pages are in this category, out of 14 total. This list may not reflect recent changes. ...

  5. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients. Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line

  6. Function (mathematics) - Wikipedia

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

    Graph of a linear function Graph of a polynomial function, here a quadratic function. Graph of two trigonometric functions: sine and cosine. A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.

  7. Julia set - Wikipedia

    en.wikipedia.org/wiki/Julia_set

    See the pictures below. Julia set (in white) for the rational function associated to Newton's method for f : z → z 3 −1. Coloring of Fatou set in red, green and blue tones according to the three attractors (the three roots of f). For some functions f(z) we can say beforehand that the Julia set is a fractal and not a simple curve. This is ...

  8. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    This can be proved as follows. First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots. As a cubic polynomial has three roots (not necessarily distinct) by the fundamental theorem of algebra, at least one root must be real.

  9. Legendre polynomials - Wikipedia

    en.wikipedia.org/wiki/Legendre_polynomials

    Legendre polynomials are also useful in expanding functions of the form (this is the same as before, written a little differently): + = = (), which arise naturally in multipole expansions. The left-hand side of the equation is the generating function for the Legendre polynomials.