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We give an approximate formula for the distribution of the largest eigenvalueof real Wishart matrices by the expected Euler characteristic method for thegeneral dimension. The formula is expressed in terms of a definite integralwith parameters. We derive a differential equation satisfied by the integralfor the $2 \times 2$ matrix case and perform a numerical analysis of it.

Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Non-central Wishart Matrix