Geodesic
Polynomials associated with reciprocation
Journal of integer sequences, Tome 12 (2009) no. 3
Polynomials are defined recursively in various ways associated with reciprocation; e.g., $S_{n+1}(x)/T_{n+1}(x) = S_{n}(x)/T_{n}(x) \pm T_{n}(x)/S_{n}(x)$. Under certain conditions, the zeros of $S_{n}$ interlace those of $T_{n}$. Identities for $S_{n}, T_{n}$ and related polynomials are derived, as well as recurrence relations and infinite sums involving roots of polynomials.
Classification : 26C10, 26C15
Keywords: polynomial, interlacing zeros 
@article{JIS_2009__12_3_a0,
     author = {Kimberling,  Clark},
     title = {Polynomials associated with reciprocation},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {3},
     zbl = {1258.11053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a0/}
}
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Kimberling,  Clark. Polynomials associated with reciprocation. Journal of integer sequences, Tome 12 (2009) no. 3. http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a0/