On the expansion of as a sum of zonal polynomials |
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Authors: | HB Kushner |
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Institution: | Information Sciences Division, The Nathan S. Kline Institute for Psychiatric Research, Orangeburg, New York 10962 USA |
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Abstract: | The coefficients aτ?, sometimes called “generalized binomial coefficients” in the expansion , are computed explicitly when t = r + 1, where ? is a partition of r and τ a partition of t. A recursion formula permits the calculation of the general aτ?. Several properties of aτ? are proved. A connection between the aτ? and other coefficients is established. The main tools used are Bingham's identity, results from the theory of invariant differential operators, and a lemma concerning zonal polynomials. |
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Keywords: | 62H99 33A70 Zonal polynomials generalized binomial coefficients invariant differential operators |
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