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We provide a proof to a recent conjecture by Forrester [2014 J. Phys. A:Math. Theor. 47, 065202] regarding the algebraic and arithmetic structure ofMeijer G-functions which appear in the expression for probability of alleigenvalues real for product of two real Gaussian matrices. In the process wecome across several interesting identities involving Meijer G-functions.

Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for product of two Gaussian matrices