Positivity of basic sums of ultraspherical polynomials
We determine the maximum ränge of A for the positivity of sums n 53 /-<\ii\ ' where C^(x) is the ultraspherical polynomial of degree n and order A. k=o ^ki^) This result resolves a problem posed by Szegö thirty five years ago. AMS 1991 Classification numbers: Primary 33C45 33C55, Secondary 42C05.