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The strong asymptotic formula for the leading coe_cient of the polynomials that are orthonormal on the system of intervals on the real line with respect to a varying weight is obtained.The dependence of the weight on the number of the polynomial is of exponential type,and the form of the weight corresponds to the \hard-edge case".The obtained formula is absolutely similar to classical Widoms formula for the weight that does not depend on the number of the polynomial.