Calculation of a certain determinant (Q5940520)

The probability density of the determinant (PDD) of matrices whose elements are Gaussian random variables are considered and the determinant of the form \(\text{det}[(a+ j-i)\Gamma(b+ j+i)]\) is calculated. The Mellin transform of the PDD of a random quaternion self-dual matrix taken from the Gaussian symplectic ensemble is calculated at first. Then the inverted Mellin transform gives the PDD.