Examples of using Hypergeometric in English and their translations into Romanian
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Multivariate hypergeometric distribution.
Such a function, andits analytic continuations, is called the hypergeometric function.
It is known as the hypergeometric differential equation.
Formula_85 (physicists')where formula_86 is Whittaker's confluent hypergeometric function.
The bilateral hypergeometric series pHp is defined by: where: is the rising factorial or Pochhammer symbol.
Random variables anddiscrete laws of probability(binomial, hypergeometric, Poisson, Pascal, geometric).
The unilateral basic hypergeometric series is defined as: where: and where: is the q-shifted factorial.
In the denominator(summed over all integers n, including negative) is called the bilateral hypergeometric series.
Yeah, we're giving a joint lecture today on multivariate hypergeometric distribution, and we haven't even begun to prepare.
If the ratio of successive terms is a rational function of qn,then the series is called a basic hypergeometric series.
However, the use of the term hypergeometric series is usually restricted to the case where the series defines an actual analytic function.
In particular, it may be useful to have, in the set of antiderivatives,the special functions of physics(like the Legendre functions, the hypergeometric function, the Gamma function, the Incomplete Gamma function and so on- see Symbolic integration for more details).
The generalized hypergeometric and Bessel functions are transcendental in general, but algebraic for some special parameter values.
Changed probability calculations for Binomial,Poisson, and Hypergeometric distributions to use Catherine Loader's saddle point approximations.
The ordinary hypergeometric series should not be confused with the basic hypergeometric series, which, despite its name, is a rather more complicated and recondite series.
There are several such generalizations of the ordinary hypergeometric series, including the ones coming from zonal spherical functions on Riemannian symmetric spaces.
The bilateral hypergeometric series fails to converge for most rational functions, though it can be analytically continued to a function defined for most rational functions.
In breaking groundfor this new field, Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions and the analytic theory of continued fractions.
Another generalization, the elliptic hypergeometric series, are those series where the ratio of terms is an elliptic function(a doubly periodic meromorphic function) of n.
Formula_83 physicists'formula_84(physicists')===Relation to confluent hypergeometric functions===The Hermite polynomials can be expressed as a special case of the parabolic cylinder functions.
Their importance and role can be understood through the following example: the hypergeometric series 2F1 has the Legendre polynomials as a special case, and when considered in the form of spherical harmonics, these polynomials reflect, in a certain sense, the symmetry properties of the two-sphere or, equivalently, the rotations given by the Lie group SO(3).
The sum of these functions gives the analytic continuation of the bilateral hypergeometric series to all values of z other than 0 and 1, and satisfies a linear differential equation in z similar to the hypergeometric differential equation.