Abstract
Let ( y) a =(1− y)(1− qy)…(1− q a−1 y). We prove that the constant term of the Laurent polynomial Π 1⩽ i< j⩽ n ( x i / x j ) a i ( qx j / x i ) a j , where x 1,…, x n , q are commmuting indeterminates and a 1,…, a n are non-negative integers, equals ( q) a 1+… + a n /( q) a n . This settles in the affirmative a conjecture of George Andrews (in: R.A. Askey, ed., Theory and Applications of Special Functions, Academic Press, New York, 1975, 191–224].
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