Synonymer & Information om | Engelska ordet HYPERGEOMETRIC

Exempel på hur man kan använda HYPERGEOMETRIC i en mening

• 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 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.
• There are several such generalizations of the ordinary hypergeometric series, including the ones coming from zonal spherical functions on Riemannian symmetric spaces.
• 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.
• 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.
• multivariate hypergeometric distribution: the balls are not returned to the urn once extracted, but with balls of more than two colors.
• 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 Laguerre polynomials may be defined in terms of hypergeometric functions, specifically the confluent hypergeometric functions, as.
• The final equalities in both of the above lines are well-known identities relating the confluent hypergeometric function with the Bessel functions.
• 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:.
• 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.
• Mary Celine Fasenmyer (1906–1996), Catholic nun whose research on hypergeometric functions prefigured WZ theory.
• 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.
• 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.
• These include primes, pseudoprimes, graph colorings, Euler numbers, continued fractions, Stirling numbers, Pythagorean triples, Ramsey theory, Lucas-Bernoulli numbers, quadratic residues, higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities, Diophantine equations, special matrices and determinants, the Collatz sequence, public-key crypto functions, elliptic curves, fractal dimension, hypergeometric functions, Fibonacci polytopes, geometry, graph theory, music, and art.
• 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 classical spectral theory of ordinary differential equations applied to the hypergeometric equation (Mehler, Weyl, Fock);.
• The bilateral hypergeometric series can be analytically continued to a multivalued meromorphic function of several variables whose singularities are.

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