- polygamma function
- полигамма функция f
English-Russian Dictionary on Probability, Statistics, and Combinatorics. — Philadelphia and Moscow. Society for Industrial and Applied Mathematics and TVP Science Publishers. K. A. Borovkov. 1994.
polygamma function
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Polygamma function — In mathematics, the polygamma function of order m is defined as the ( m + 1)th derivative of the logarithm of the gamma function::psi^{(m)}(z) = left(frac{d}{dz} ight)^m psi(z) = left(frac{d}{dz} ight)^{m+1} lnGamma(z).Here :psi(z) =psi^{(0)}(z) … Wikipedia
Polygamma-Funktion — In der Mathematik sind die Polygamma Funktionen eine Reihe spezieller Funktionen, die als die Ableitungen der Funktion logΓ(x) definiert sind. Dabei bezeichnet Γ(x) die Gammafunktion. Die ersten beiden Polygammafunktionen werden Digammafunktion… … Deutsch Wikipedia
Polygamma-Funktionen — In der Mathematik sind die Polygamma Funktionen eine Reihe spezieller Funktionen, die als die Ableitungen der Funktion logΓ(x) definiert sind. Dabei bezeichnet Γ(x) die Gammafunktion. Die ersten beiden Polygammafunktionen werden Digammafunktion… … Deutsch Wikipedia
Digamma function — For Barnes s gamma function of 2 variables, see double gamma function. Digamma function ψ(s) in the complex plane. The color of a point s encodes the value of ψ(s). Strong colors denote values close to zero and hue encodes the value s argument … Wikipedia
Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… … Wikipedia
Hurwitz zeta function — In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. It is formally defined for complex arguments s with Re( s )>1 and q with Re( q )>0 by:zeta(s,q) = sum {n=0}^infty frac{1}{(q+n)^{sThis series … Wikipedia
Trigamma function — In mathematics, the trigamma function, denoted psi;1(z), is the second of the polygamma functions, and is defined by: psi 1(z) = frac{d^2}{dz^2} lnGamma(z).It follows from this definition that: psi 1(z) = frac{d}{dz} psi(z)where psi;(z) is the… … Wikipedia
Dirichlet beta function — This article is about the Dirichlet beta function. For other beta functions, see Beta function (disambiguation). In mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the… … Wikipedia
Multiple gamma function — For derivatives of the log of the gamma function, see polygamma function. In mathematics, the multiple gamma function ΓN is a generalization of the Euler Gamma function and the Barnes G function. The double gamma function was studied Barnes… … Wikipedia
Multivariate gamma function — In mathematics, the multivariate Gamma function, Γp(·), is a generalization of the Gamma function. It is useful in multivariate statistics, appearing in the probability density function of the Wishart and Inverse Wishart distributions. It has two … Wikipedia
Multiplication theorem — In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various… … Wikipedia
