Synonymer & Information om | Engelska ordet HYPERGEOMETRIC

Exempel på hur man kan använda HYPERGEOMETRIC i en mening

• In general, the arc length of the lituus spiral cannot be expressed as a closed-form expression, but the arc length of the lituus spiral can be represented as a formula using the Gaussian hypergeometric function:.
• They also have numerous applications with regard to the summation of hypergeometric series, summations involving the inverse of the central binomial coefficient, sums of the polygamma function, and Dirichlet L-series.
• There are some "noncentral distributions" that are not usually formulated in terms of a "noncentrality parameter": see noncentral hypergeometric distributions, for example.
• It is possible to solve the quintic equation if general hypergeometric functions are included, although the solution is far too complicated algebraically to be useful.
• The bilateral hypergeometric series can be analytically continued to a multivalued meromorphic function of several variables whose singularities are.
• A more restricted class of sextics can be solved by the one-variable generalised hypergeometric function using Felix Klein's approach to solving the quintic equation.
• the classical spectral theory of ordinary differential equations applied to the hypergeometric equation (Mehler, Weyl, Fock);.
• Agner Fog (2007, 2008) suggested that the best way to avoid confusion is to use the name Wallenius' noncentral hypergeometric distribution for the distribution of a biased urn model in which a predetermined number of items are drawn one by one in a competitive manner and to use the name Fisher's noncentral hypergeometric distribution for one in which items are drawn independently of each other, so that the total number of items drawn is known only after the experiment.
• This class of functions is stable under sums, products, differentiation, integration, and contains many usual functions and special functions such as exponential function, logarithm, sine, cosine, inverse trigonometric functions, error function, Bessel functions and hypergeometric functions.
• The final equalities in both of the above lines are well-known identities relating the confluent hypergeometric function with the Bessel functions.
• Weyl applied his theory to Carl Friedrich Gauss's hypergeometric differential equation, thus obtaining a far-reaching generalisation of the transform formula of Gustav Ferdinand Mehler (1881) for the Legendre differential equation, rediscovered by the Russian physicist Vladimir Fock in 1943, and usually called the Mehler–Fock transform.
• The general solutions to the above second-order differential equations are in fact linear combinations of both Hermite polynomials and confluent hypergeometric functions of the first kind.
• In fact more is true: Schwarz's list underlies all second-order equations with regular singularities on compact Riemann surfaces having finite monodromy, by a pullback from the hypergeometric equation on the Riemann sphere by a complex analytic mapping, of degree computable from the equation's data.
• The univariate noncentral hypergeometric distribution may be derived alternatively as a conditional distribution in the context of two binomially distributed random variables, for example when considering the response to a particular treatment in two different groups of patients participating in a clinical trial.
• The characteristic function of the Dirichlet distribution is a confluent form of the Lauricella hypergeometric series.
• The monodromy of a hypergeometric equation describes how fundamental solutions change when analytically continued around paths in the z plane that return to the same point.
• When n = 2, the Lauricella functions correspond to the Appell hypergeometric series of two variables:.
• multivariate hypergeometric distribution: the balls are not returned to the urn once extracted, but with balls of more than two colors.
• If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.
• The aim of ORA is to identify such enriched pathways, judging by statistical significance of the overlap between FGS and AGS as determined either by an appropriate statistic, such as Jaccard index or by a statistical test producing p-values (Fisher's exact test or the test using hypergeometric distribution).

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