Asymptotics of multinomial sums and identities between multi-integrals
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We calculate the asymptotics of combinatorial sums ∑ α f(α)( α n ) β , whereα = (α 1, …,α h ) withα i =α j for certaini, j. Hereh is fixed and theα i ’s are natural numbers. This implies the asymptotics of the correspondingS n -character degrees ∑λ f(λ)d λ β . For certain sequences ofS n 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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