Examples of "dirichlet"
If "a" is a Dirichlet character then its Dirichlet series generating function is called a Dirichlet L-series.
the Dirichlet process reduces to a Dirichlet distribution.
It also is the Dirichlet -series of the non-principal Dirichlet character of modulus 4 evaluated at , and therefore the value of the Dirichlet beta function.
The best known Dirichlet form is the Dirichlet energy of functions on formula_20
Dirichlet characters are named in honour of Peter Gustav Lejeune Dirichlet.
Dirichlet processes are frequently used in Bayesian nonparametric statistics. The Imprecise Dirichlet Process
The Dirichlet process can also be seen as the infinite-dimensional generalization of the Dirichlet distribution. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions. A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models.
the Dirichlet lambda function (closely related to the Dirichlet eta function)
The infinite-dimensional generalization of the Dirichlet distribution is the "Dirichlet process".
Dirichlet lies on the eastern margin of the Dirichlet-Jackson Basin.
If formula_2 is a Dirichlet character, one defines its Dirichlet "L"-series by
The dual Dirichlet problem can be used to solve the Dirichlet problem:
formula_30 defined above is given by formula_31. Thus Dirichlet forms are natural generalizations of the Dirichlet integrals
be the corresponding Dirichlet series. Presume the Dirichlet series to be uniformly convergent for formula_3. Then Perron's formula is
Clearly, the equation inside the integration has the same form as the Dirichlet distribution. According to the Dirichlet distribution,
In mathematics, the Dirichlet space on the domain formula_1 (named after Peter Gustav Lejeune Dirichlet), is the reproducing kernel Hilbert space of holomorphic functions, contained within the Hardy space formula_2, for which the "Dirichlet integral", defined by
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of formula_1. Dirichlet characters are used to define Dirichlet "L"-functions, which are meromorphic functions with a variety of interesting analytic properties.
The Dirichlet convolution can be defined for general arithmetic functions, and yields a ring structure, the Dirichlet ring.
In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet.
In 1855 Dirichlet was awarded the civil class medal of the Pour le Mérite order at von Humboldt's recommendation. The Dirichlet crater on the Moon and the 11665 Dirichlet asteroid are named after him.