Browsing by Author "Brown, G."

Now showing items 1-6 of 6

    • Article  

      A new bound for the Fejér-Jackson sum 

      Brown, G.; Koumandos, S. (1998)
      We establish a new positive functional estimate for the FejérJackson sum Sn(θ) = Σnk=1 k-1 sin kθ. This result enables us to give a simple proof of a result of Askey and Steinig on a monotonic sine sum associated with the ...
    • Article  

      On a monotonic trigonometric sum 

      Brown, G.; Koumandos, S. (1997)
      By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of Σk-1 cos kθ.
    • Article  

      On the positivity of some basic legendre polynomial sums 

      Brown, G.; Koumandos, S.; Wang, K. (1999)
      The positivity of the partial sums of the series of Legendre polynomials is a classical result of Fejér. The paper presents corresponding results for both even and odd Legendre polynomials with best possible leading ...
    • Article  

      Positivity of basic sums of ultraspherical polynomials 

      Brown, G.; Koumandos, S.; Wang, K. -Y (1998)
      We determine the maximum range of A for the positivity of sums This result resolves a problem posed by Szegö thirty five years ago. © 2014, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All ...
    • Article  

      Positivity of Cotes numbers at more Jacobi abscissas 

      Brown, G.; Koumandos, S.; Wang, K. -Y (1996)
      The positivity of certain finite sums of even ultraspherical polynomials has been identified by Askey as a specially interesting case of a more general problem concerning positivity of Cotes numbers at Jacobi abscissas. ...
    • Article  

      Positivity of more Jacobi polynomial sums 

      Brown, G.; Koumandos, S.; Wang, K. -Y (1996)