On a conjecture for trigonometric sums and starlike functions

  • Authors:

  • Stamatis Koumandos;Stephan Ruscheweyh

  • Affiliations:

  • Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus;Mathematisches Institut, Universität Würzburg, 97074 Würzburg, Germany

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2007

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Abstract

We pose and discuss the following conjecture: let s"n^@m(z)@?@?"k"="0^n(@m)"kk!z^k, and for @r@?(0,1] let @m^*(@r) be the unique solution @m@?(0,1] of @!"0^(^@r^+^1^)^@psint-@r@pt^@m^-^1dt=0.Then for 0