Journal of Integer Sequences, Vol. 12 (2009), Article 09.3.4

Polynomials Associated with Reciprocation

Clark Kimberling
Department of Mathematics
University of Evansville
1800 Lincoln Avenue
Evansville, IN 47722


Polynomials are defined recursively in various ways associated with reciprocation; e.g., Sn+1(x)/Tn+1(x) = Sn(x)/Tn(x) ± Tn(x)/Sn(x). Under certain conditions, the zeros of Sn interlace those of Tn. Identities for Sn, Tn and related polynomials are derived, as well as recurrence relations and infinite sums involving roots of polynomials.

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(Concerned with sequences A073833 A095704 A096754 A108086 A127814 A135670 A135685 A141665 A147985 A147986 A147987 A147988 A154308 and A154310.)

Received January 11, 2008; revised version received March 18 2009. Published in Journal of Integer Sequences, March 20 2009.

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