Upper approximations are derived for the absolute values of single and double Dirichlet averages of xⁿ. These averages are homogeneous polynomials of degree n in several complex variables. Special cases yield upper approximations to the absolute value of a Jacobi polynomial with any complex values of the indices and argument. A Jacobi polynomial is represented in a new way by a triple sum.
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B. C. Carlson (1974) studied this question.
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