On bounds for solutions of monotonic first order difference-differential systems

@article{Segura2011OnBF,
  title={On bounds for solutions of monotonic first order difference-differential systems},
  author={Javier Segura},
  journal={Journal of Inequalities and Applications},
  year={2011},
  volume={2012},
  pages={1-17}
}
  • J. Segura
  • Published 4 October 2011
  • Mathematics
  • Journal of Inequalities and Applications
Many special functions are solutions of first order linear systems yn′(x)=an(x)yn(x)+dn(x)yn-1(x),yn-1′(x),=bn(x)yn-1(x)+en(x)yn(x). We obtain bounds for the ratios yn(x)/yn-1(x) and the logarithmic derivatives of yn(x) for solutions of monotonic systems satisfying certain initial conditions. For the case dn(x)en(x) > 0, sequences of upper and lower bounds can be obtained by iterating the recurrence relation; for minimal solutions of the recurrence these are convergent sequences. The bounds are… 

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