Positivity of Cotes numbers at more Jacobi abscissas (Q1921387)

Let \(P_n^{(\alpha, \beta)} (x)\) the \(n\)-th Jacobi polynomial and consider the expansion \[ (1-x)^{-\gamma} (1+x)^{-d}\sim \sum^\infty_{k=0} a_k P_n^{(\alpha, \beta)}(x). \] The authors study the positivity of the partial sums \(S_n= \sum^n_{k=0} a_k P_n^{(\alpha, \beta)}(x)\), \(-1\leq x\leq 1\), \(n=0, 1,\dots\), and establish some new cases of positivity of such sums.