THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. I

1990 ◽  
Vol 35 (3) ◽  
pp. 543-571 ◽  
Author(s):  
A N Varchenko
Keyword(s):  
Beta Function ◽  
Critical Values ◽  
Linear Functions ◽  
Vandermonde Determinant ◽  
Euler Beta Function

COMPARISON BETWEEN POLYNOMIAL, EULER BETA-FUNCTION AND EXPO-RATIONAL B-SPLINE BASES

2011 ◽  
Author(s):  
Arnt R. Kristoffersen ◽  
Lubomir T. Dechevsky ◽  
Arne Lakså ◽  
Bo̸rre Bang ◽  
George Venkov ◽  
...  
Keyword(s):  
Beta Function ◽  
B Spline ◽  
Euler Beta Function

scholarly journals An Investigation on the Beta Function III: Explicit Evaluation of the Harmonic Number H3/2

2014 ◽  
Vol 9 ◽  
pp. 1-2
Author(s):  
Edigles Guedes ◽  
K. Raja Rama Gandhi
Keyword(s):  
Closed Form ◽  
Beta Function ◽  
Harmonic Number ◽  
Explicit Evaluation ◽  
Euler Beta Function

In previous paper, we developed new versions of the Euler beta function, which given a closed form for the harmonic number H3/2.

scholarly journals ENCODING THE SCALING OF THE COSMOLOGICAL VARIABLES WITH THE EULER BETA FUNCTION

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4917-4924 ◽  
Author(s):  
M. A. PER ◽  
A. J. SEGUÍ
Keyword(s):  
Equation Of State ◽  
Beta Function ◽  
Cosmological Models ◽  
Physical Variable ◽  
Scaling Exponent ◽  
Singular Behavior ◽  
Scaling Exponents ◽  
Euler Beta Function

We study the scaling exponents for the expanding isotropic flat cosmological models. The dimension of space, the equation of state of the cosmic fluid and the scaling exponent for a physical variable are related by the Euler Beta function that controls the singular behavior of the global integrals. We encounter dual cosmological scenarios using the properties of the Beta function. When we study the integral of the density of entropy we reproduce the Fischler–Susskind holographic bound.

A generalization of the Euler beta function and applications

2011 ◽  
Vol 18 (2) ◽  
pp. 271-298
Author(s):  
Ilia Lomidze
Keyword(s):  
Special Functions ◽  
Beta Function ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Euler Formula ◽  
Euler Beta Function ◽  
Dimensional Variable

Abstract A generalization of the Euler beta function to the case of a multi-dimensional variable is defined. In this context, the original beta function is a function of a two-dimensional variable. An analogue of the Euler formula for this new function is derived for the case of a three-dimensional variable. Based on the derived formula, a number of relations for the Gauss hypergeometrical function are obtained. Moreover, the analytic formulae for some new integrals of special functions are obtained.

scholarly journals Celestial operator products of gluons and gravitons

2021 ◽  
pp. 2140003
Author(s):  
Monica Pate ◽  
Ana-Maria Raclariu ◽  
Andrew Strominger ◽  
Ellis Ye Yuan
Keyword(s):  
Operator Product Expansion ◽  
Beta Function ◽  
Tree Level ◽  
Operator Product ◽  
Recursion Relations ◽  
Yang Mills ◽  
Euler Beta Function ◽  
Celestial Sphere ◽  
Asymptotic Symmetries

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein–Yang–Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.

scholarly journals An Investigation on the Beta Function I: New Versions of the Euler Beta Function

2014 ◽  
Vol 7 ◽  
pp. 41-46
Author(s):  
Edigles Guedes ◽  
Raja Rama Gandhi
Keyword(s):  
Beta Function ◽  
Euler Beta Function

We developed new versions of the Euler beta function.

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