Dirichlet beta function information

mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function. It is a...

tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred...

multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly...

Synchrotron function Riemann zeta function: A special case of Dirichlet series. Riemann Xi function Dirichlet eta function: An allied function. Dirichlet beta function...

mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial...

for the beta prime distribution. The generalization to multiple variables is called a Dirichlet distribution. The probability density function (PDF) of...

In natural language processing, latent Dirichlet allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) for modeling...

(\operatorname {Re} (s)>1).} The polylogarithm is related to Dirichlet eta function and the Dirichlet beta function: Li s ⁡ ( − 1 ) = − η ( s ) , {\displaystyle \operatorname...

and rings) Dirichlet algebra Dirichlet beta function Dirichlet boundary condition (differential equations) Neumann–Dirichlet method Dirichlet characters...

In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes...

} the Dirichlet boundary conditions on the interval [a,b] take the form y ( a ) = α , y ( b ) = β , {\displaystyle y(a)=\alpha ,\quad y(b)=\beta ,} where...

{(-1)^{n-1}}{n^{s}}}} The Dirichlet beta function: β ( s ) = 2 − s Φ ( − 1 , s , 1 / 2 ) = ∑ k = 0 ∞ ( − 1 ) k ( 2 k + 1 ) s {\displaystyle \beta (s)=2^{-s}\Phi...

generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions...

Multinomial logistic regression Dirichlet distribution – an alternative way to sample categorical distributions Partition function Exponential tilting – a generalization...

analysis, the Dirichlet kernel, named after the German mathematician Peter Gustav Lejeune Dirichlet, is the collection of periodic functions defined as D...

In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by χ ν ( z ) = ∑ k = 0 ∞ z 2 k +...

{\displaystyle \operatorname {Ti} _{n}(1)=\beta (n)} , where β ( s ) {\displaystyle \beta (s)} represents the Dirichlet beta function. The inverse tangent integral...

{\displaystyle MGB1(y;a=1,b=1,p,q)} , the multivariate inverted beta and inverted Dirichlet (Dirichlet type 2) distribution given by M G B 2 ( y ; a = 1 , b =...

example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers. The indicator function of a subset A...

proved to be irrational). Catalan's constant, and the values of Dirichlet beta function at other even integers, β(4), β(6), ... (not even proven to be...

B ( x , y ) {\displaystyle B(x,y)} denotes the Beta function. This reduces to the standard Dirichlet distribution if b i − 1 = a i + b i {\displaystyle...