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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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New integral inequalities for preinvex functions via generalized beta function
Journal of Interdisciplinary Mathematics, 2019In this study, we establish some new integral inequalities for the logarithmically p-preinvex functions by using generalizes beta function. This work extends and generalized the results appeared in the literature.
P. Mohammed
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Approximate gamma–beta type functions
Nonlinear Analysis: Theory, Methods & Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lee, Young Whan, Kim, Gwang Hui
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Normalized Incomplete Beta Function: Log-Concavity in Parameters and Other Properties
, 2015The logarithmic concavity/convexity in parameters of the normalized incomplete beta function has been established by Finner and Roters in 1997 as a corollary of a rather difficult result, based on generalized reproductive property of certain ...
D. Karp
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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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Ergodic Theory and Dynamical Systems, 1994
AbstractThe pointwise spectral radii of irreducible matrices whose entries are polynomials with positive, integral coefficients are studied in this paper. Most results are derived in the case that the resulting algebraic function, the beta function of S. Tuncel, is in fact a polynomial.
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AbstractThe pointwise spectral radii of irreducible matrices whose entries are polynomials with positive, integral coefficients are studied in this paper. Most results are derived in the case that the resulting algebraic function, the beta function of S. Tuncel, is in fact a polynomial.
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