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Some results on the beta function and the incomplete beta function
Asian-European Journal of Mathematics, 2015The incomplete Beta function [Formula: see text] is defined for [Formula: see text] and [Formula: see text]. This definition was extended to negative integer values of [Formula: see text] and [Formula: see text] by Özçaḡ et al. using neutrix limits. Partial derivatives of the incomplete Beta function [Formula: see text] for negative integer values of [
Lin, Mongkolsery +2 more
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The American Mathematical Monthly, 1951
The First Eulerian Integral, called the Beta Function, is defined by B(x, y) =folt-1(1 -t)Y-ldt, which converges for x > 0 and y > 0. The well-known equation connecting the Beta and Gamma functions, B(x, y) = r(x)r(y)/r(x+y), is therefore valid only for positive real x and y. However, this relation is commonly used as a definition, to extend B(x, y) so
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The First Eulerian Integral, called the Beta Function, is defined by B(x, y) =folt-1(1 -t)Y-ldt, which converges for x > 0 and y > 0. The well-known equation connecting the Beta and Gamma functions, B(x, y) = r(x)r(y)/r(x+y), is therefore valid only for positive real x and y. However, this relation is commonly used as a definition, to extend B(x, y) so
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An Essay on Bion's Beta Function
The Psychoanalytic Review, 2013Among the major theorists studying the effect of the external world on the individual, none had a more ambiguous relationship to the psychic manifestations of the environment than Wilfred Bion. On the one hand his theory of the mind contained a new concept, beta elements, to depict the intrusion of the material world into the mental sphere, while on ...
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Gamma Functions, Beta Functions, and Related
2021Topics of this chapter are gamma functions, beta functions, and related functions in the complex domain. The evaluations are based on various numerical techniques in dependence of the function argument. Related functions are the Pochhammer symbol, the psi or digamma function, the incomplete gamma function and its first and second derivative, the ...
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Determination of Beta-Cell Function: Ion Channel Function in Beta Cells
2012For the regulation of beta-cell function ion channels are of outstanding importance. Beta cells are specialized to convert changes in blood glucose concentration to an adequate secretory response. To achieve this, nutrient-induced alterations of electrical activity are directly coupled to changes in insulin release.
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On \(\delta -\beta \)-continuous functions
2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hatir, E., Noiri, T.
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Russian Mathematical Surveys, 2001
Recently, \textit{V. Spiridonov} and \textit{A. Zhedanov} [Commun. Math. Phys. 210, No. 1, 49--83 (2000; Zbl 0989.30008)] considered a finite-dimensional class of some biorthogonal rational functions with a discrete measure. Here, in the paper under review, the author proves an elliptic generalization of the familiar basis (or \(q\)-) beta integral ...
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Recently, \textit{V. Spiridonov} and \textit{A. Zhedanov} [Commun. Math. Phys. 210, No. 1, 49--83 (2000; Zbl 0989.30008)] considered a finite-dimensional class of some biorthogonal rational functions with a discrete measure. Here, in the paper under review, the author proves an elliptic generalization of the familiar basis (or \(q\)-) beta integral ...
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1982
We use the notation of Chapter 22. In all cases the dimension of W f0 is 1 but 1/(1 − x) is not a representative of the basis unless condition (22.1.1) is satisfied. This means that the formulae for the dual space will degenerate if (22.1.1) is not satisfied.
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We use the notation of Chapter 22. In all cases the dimension of W f0 is 1 but 1/(1 − x) is not a representative of the basis unless condition (22.1.1) is satisfied. This means that the formulae for the dual space will degenerate if (22.1.1) is not satisfied.
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Nielsen's beta function and some infinitely divisible distributions
Mathematische Nachrichten, 2021Christian Berg, Stamatis Koumandos
exaly
2020
The Beta function is part of a special function in the form of an integral statement and the result form is twice the multiplication of factorial functions. The Beta function is part of an unnatural integral because it has infinite-value parameters, resulting in infinite functions.
mustika, yulia, cut
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The Beta function is part of a special function in the form of an integral statement and the result form is twice the multiplication of factorial functions. The Beta function is part of an unnatural integral because it has infinite-value parameters, resulting in infinite functions.
mustika, yulia, cut
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