Abstract:
The behavior of the graph of the function $Z_n(t)=\|Z'_n(\cdot,t)\|/\|Z_n(\cdot,t)\|$ is discussed in the case where the functions $Z_n(x,t)$ are the Zolotarev polynomials and the norm is a weighted sup-norm. Based on calculations performed for various weights, it is conjectured that the characteristic jump in $Z_n(t)$ in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the midpoint of the interval.
Key words:Zolotarev polynomials, sup-norm, numerical study of the behavior of Zolotarev polynomials, Laguerre weight function.
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