Polynomials Associated with Reciprocation
Clark Kimberling
Department of Mathematics
University of Evansville
1800 Lincoln Avenue
Evansville, IN 47722
USA
Abstract:
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.
Full version: pdf,
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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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