Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomials

@article{Karp2012PositivityOT,
  title={Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomials},
  author={Dmitry B. Karp},
  journal={Journal of Mathematical Sciences},
  year={2012},
  volume={193},
  pages={106-114}
}
  • D. Karp
  • Published 7 March 2012
  • Mathematics
  • Journal of Mathematical Sciences
In this note, we prove the positivity of Maclaurin coefficients of polynomials written in terms of rising factorials and arbitrary log-concave sequences. These polynomials arise naturally in studying log-concavity of rising factorial series. Several conjectures concerning zeros and coefficients of a generalized form of those polynomials are advanced. Also polynomials whose generating functions are higher-order Toeplitz determinants formed by rising factorial series are considered. Three… 
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