Some polynomials that are hard to compute

Using the result of Heintz and Sieveking 1], we show that the polynomials $\text{Σ}{}_{\mathrm{1?j?d}}\text{b}{}^{\mathrm{<mtext>1</mtext><mtext>i</mtext>}}\text{X}{}^{\mathrm{j}}$ with b positive real different from one, and Σ_1?j?dj^rX^j with r rational not integer, are hard to compute.