Asymptotics of multinomial sums and identities between multi-integrals
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We calculate the asymptotics of combinatorial sums ∑αf(α)(αn)β, whereα = (α1, …,αh) withαi =αj for certaini, j. Hereh is fixed and theαi’s are natural numbers. This implies the asymptotics of the correspondingSn-character degrees ∑λf(λ)dλβ. For certain sequences ofSn characters which involve Young’s rule, the latter asymptotics were obtained earlier  by a different method. Equating the two asymptotics, we obtain equations between multi-integrals which involve Gaussian measures. Special cases here give certain extensions of the Mehta integral , .
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