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Abstract  This paper studies, by employing analytical tools, the small‐time behavior of the heat content for the Poisson kernel over the unit ball in    R  d   ,    d  ⩾  2    by working with its related set covariance function. As a result, we obtain a representation for the third term in the expansion of the heat content over the unit ball and provide the explicit form of this term in the particular cases    d  =  2    and    d  =  3   .

On the heat content for the Poisson kernel over the unit ball in the euclidean space