Browsing by Subject "Positive cosine sums"

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    • Article  

      Positive Gegenbauer polynomial sums and applications to starlike functions 

      Koumandos, S.; Ruscheweyh, S. (2006)
      Let sn(f,z):=∑k=0n akz k be the nth partial sum of f(z)= ∑k=0 ∞ akzk. We show that Re s n(f/z,z)>0 holds for all z ∈ D, n ∈ N, and all starlike functions f of order λ iff λ0 ≤ λ 0 for all n ∈ N, x ∈ [-1,1], and 0 < μ ≤ ...