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Weingarten function
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<p>In mathematics, Weingarten functions are <a href="/facts/Rational_function/2nJGu0Ko">rational functions</a> indexed by <a href="/facts/Integer_partition/LtyXWqwH">partitions of integers</a> that can be used to calculate integrals of products of matrix coefficients over <a href="/facts/Classical_group/TEV7cSvJ">classical groups</a>. They were first studied by Weingarten (1978) who found their asymptotic behavior, and named by Collins (2003), who evaluated them explicitly for the <a href="/facts/Unitary_group/lEvudIhU">unitary group</a>. </p>