The celebrated Mehta integral is shown to be equivalent to a simple algebraic-differential identity, which is completely routine for any fixed number of variables. Askey [As] proposed the problem of proving the Mehta (see [M]) integral identity (Mehta) 2 1 exp(-x/2 xnl2 H (xi-xj)2Cdxl""dan-H (cj)! without using Selberg's integral (see [M]). This problem was solved by Anderson [An]. Here we use ...

In this note we give a proof of Cherednik’s generalization of Macdonald–Mehta identities for the root system An−1, using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a “difference analogue of the Gaussian measure”. They were suggested by Cherednik, who also gave a proof based on represen...

1Department of Nephrology, Transplantation Medicine and Immunology, G. R. Doshi and K. M. Mehta Institute of Kidney Diseases & Research Centre [IKDRC],Ahmedabad, Gujarat, India 2Department of Pathology, Laboratory Medicine, Transfusion Services, Immunohematology, G. R. Doshi and K. M. Mehta Institute of Kidney Diseases & Research Centre [IKDRC],Ahmedabad, Gujarat, India 3Senior Research Officer...

Abstract: Solar, wind and other renewable energy sources are becoming an important part of energy supply to the power grid. Integrating a Hybrid Energy Storage Systems (HESS) with renewable energy sources can make these intermittent renewable energy sources more dispatchable. The HESS will play a vital and large role in renewable energy based 3-phase 4-wire grid connected electrical power infra...