Itiswell-knownthatifpisahomogeneouspolynomialofdegreekinnvariables,p∈Pk,thentheordinaryderivativep(■)(r^2-n)hastheformAn,kY(x)r2-n-2kwhereAn,kisaconstantandwhereYisaharmonichomogeneouspolynomialofdegreek,Y∈Hk,actuallytheprojectionofpontoHk.Herewestudythedistributionalderivativep(■)(r2-n)andshowthattheordinarypartisstillamultipleofY,butthatthedeltapartisindependentofY,thatis,itdependsonlyonp-Y.Wealsoshowthattheexponent2-nisspecialinthesensethatthecorrespondingresultsforp(■)(rα)donotholdifα≠2-n.Furthermore,weestablishthatharmonicpolynomialsappearasmultiplesofr^2-n-2k-2k’whenp(■)isappliedtoharmonicmultipolesoftheformY’(x)r^2-n-2k’forsomeY∈Hk.
