Hypergeometric function wikipedia - Search
Open links in new tab
  1. Wikipedia
    https://en.wikipedia.org › wiki › Hypergeometric_function

    Hypergeometric function - Wikipedia

    • In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points ca… See more

    History

    The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum.
    Hypergeometric … See more

    The hypergeometric series

    The hypergeometric function is defined for |z| < 1 by the power series
    It is undefined (or infinite) if c equals a non-positive integer. Here (q)n is the (rising) Pochhammer symbol, which is defined by:
    The series … See more

    Differentiation formulas

    Using the identity , it is shown that
    and more generally, See more

    Special cases

    Many of the common mathematical functions can be expressed in terms of the hypergeometric function, or as limiting cases of it. Some typical examples are
    When a=1 and b=c, the series reduces into a plain … See more

    The hypergeometric differential equation

    The hypergeometric function is a solution of Euler's hypergeometric differential equation
    which has three regular singular points: 0,1 and ∞. The generalization of this equation to three arbitrary regular singular points is given by … See more

    Wikipedia text under CC-BY-SA license
    Feedback
    Table of Contents
    History
    The hypergeometric series
    Differentiation formulas
    Special cases
    The hypergeometric differential equation
     
    Kizdar net | Kizdar net | Кыздар Нет
  2. Some results have been removed