On the generalized Ball bases

@article{Delgado2006OnTG,
  title={On the generalized Ball bases},
  author={Jorge Delgado and Juan Manuel Pe{\~n}a},
  journal={Advances in Computational Mathematics},
  year={2006},
  volume={24},
  pages={263-280}
}
The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>3, in contrast with the Said–Ball basis. We… 
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