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A multivariable generalization of the continuous Hahn polynomials is presented; it is a (4p+4)-parameter family, where p is the number of variables. It is shown that they are orthogonal with respect to subspaces of equal degree and biorthogonal within a given subspace. In the simplest case the multivariable weight function takes the form sech[π(x1+x2+⋅⋅⋅+xp)]sech(πx1) sech(πx2)⋅⋅⋅sech(πxp).
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M. V. Tratnik (1988) studied this question.
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