Hypergeometric

Hypergeometric

Hypergeometric can refer to various related mathematical topics:

*Hypergeometric series, "p""F""q", a power series
**Confluent hypergeometric function, 1"F"1, also known as the Kummer function
**Euler hypergeometric integral, an integral representation of 2"F"1
**Lauricella hypergeometric series, hypergeometric series of three variables
**Horn function, 34 distinct convergent hypergeometric series of order two
*Basic hypergeometric series, a generalization of the ordinary hypergeometric series
*Hypergeometric function of a matrix argument, the multivariate generalization of the hypergeometric series
*Hypergeometric differential equation, a second-order linear ordinary differential equation
*Hypergeometric distribution, a discrete probability distribution


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  • Hypergeometric series — In mathematics, a hypergeometric series is a power series in which the ratios of successive coefficients k is a rational function of k . The series, if convergent, will define a hypergeometric function which may then be defined over a wider… …   Wikipedia

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  • Hypergeometric identities — In mathematics, hypergeometric identities are equalities involving sums over hypergeometric terms, i.e. the coefficients occurring in hypergeometric series. These identities occur frequently in solutions to combinatorial problems, and also in the …   Wikipedia

  • Hypergeometric function of a matrix argument — In mathematics, the hypergeometric function of a matrix argument is a generalization of the classical hypergeometric series. It is the closed form expression of certain multivariate integrals, especially ones appearing in random matrix theory.… …   Wikipedia

  • Hypergeometric function — In mathematics, a hypergeometric function can be:* Hypergeometric series in the scalar (univariate) case and is the most common use for the term hypergeometric function* Hypergeometric function of a matrix argument in the multivariate case …   Wikipedia

  • hypergeometric series — noun Any power series such that the ratio of the (k+1) th and the k th terms is a rational function of the natural integer k. See Also: hypergeometric function, hypergeometric equation, confluent hypergeometric series, basic hypergeometric series …   Wiktionary

  • hypergeometric function — noun Any function that is a solution of the hypergeometric equation; usually an expansion of an hypergeometric series …   Wiktionary

  • hypergeometric function — Math. a function that is a solution to a hypergeometric equation. * * * …   Universalium

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