Coulson-type integral formulas for the sum of powers of absolute values of roots of polynomials

2021 ◽  
Vol 494 (2) ◽  
pp. 124650
Author(s):  
Zhibin Du
Keyword(s):  
Integral Formulas ◽  
Type Integral ◽  
Roots Of Polynomials

scholarly journals Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices

2015 ◽  
Vol 04 (02) ◽  
pp. 1550007 ◽  
Author(s):  
Patrick Desrosiers ◽  
Dang-Zheng Liu
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Theory ◽  
Direct Application ◽  
Holonomic System ◽  
Expectation Value ◽  
Linear Partial Differential Equations ◽  
Integral Formulas ◽  
Duality Relations ◽  
Selberg Integrals ◽  
Type Integral

We study a new Selberg-type integral with n + m indeterminates, which turns out to be related to the deformed Calogero–Sutherland systems. We show that the integral satisfies a holonomic system of n + m non-symmetric linear partial differential equations. We also prove that a particular hypergeometric function defined in terms of super-Jack polynomials is the unique solution of the system. Some properties such as duality relations, integral formulas, Pfaff–Euler and Kummer transformations are also established. As a direct application, we evaluate the expectation value of ratios of characteristic polynomials in the classical β-ensembles of Random Matrix Theory.

scholarly journals Integral formulas with weight factors

1992 ◽  
Vol 52 (1) ◽  
pp. 26-39
Author(s):  
Telemachos Hatziafratis
Keyword(s):  
Complete Intersection ◽  
Integral Formula ◽  
Integral Formulas ◽  
Weight Factors ◽  
Type Integral

AbstractA Bochner-Martinelli-Koppelman type integral formula with weight factors is derived on complete intersection submanifolds of domains of Cn.

Crofton-type integral formulas for star domain

1988 ◽  
Vol 28 (3) ◽  
pp. 251-258 ◽  
Author(s):  
Waldemar Cieślak
Keyword(s):  
Integral Formulas ◽  
Type Integral

scholarly journals ON GENERAL EULERIAN INTEGRAL FORMULAS AND FRACTIONAL INTEGRATION

1999 ◽  
Vol 30 (2) ◽  
pp. 155-164
Author(s):  
K. C. GUPTA ◽  
S. P. GOYAL ◽  
R. K. LADDHA
Keyword(s):  
Integral Operator ◽  
Infinite Series ◽  
Fractional Integral ◽  
Integral Formula ◽  
Polynomial System ◽  
Fractional Integration ◽  
Compact Form ◽  
Integral Formulas ◽  
Special Cases ◽  
Type Integral

In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1], [3], [4], [5], [9], [11], etc.) and new results. Since the integral has been given in a compact form free from infinite series, it is likely to prove useful in applications. Three special cases of the main integral (which are also sufficiently general in nature and are of interest in themselves) have also been given. Finally, the main integral formula has been expressed as a fractional integral operator to make it more useful in applications.

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