Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences

Stieltjes interlacing states that if { p n ( z ) } n = 0 ∞ is a sequence of orthogonal polynomials, then there is at least one zero of p n ( z ) in between any two consecutive zeros of p m ( z ), where m < n − 1. Stieltjes interlacing holds for the zeros of polynomials from different sequences of...

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Veröffentlicht in:Numerical algorithms 2023, Vol.92 (1), p.723-746
Hauptverfasser: Kar, Pinaki Prasad, Jordaan, Kerstin, Gochhayat, Priyabrat
Format: Artikel
Sprache:eng
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Zusammenfassung:Stieltjes interlacing states that if { p n ( z ) } n = 0 ∞ is a sequence of orthogonal polynomials, then there is at least one zero of p n ( z ) in between any two consecutive zeros of p m ( z ), where m < n − 1. Stieltjes interlacing holds for the zeros of polynomials from different sequences of little q -Jacobi polynomials p n ( z ; a , b | q ), 0 < a q
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01387-8