Log-Concavity of Recursively Defined Polynomials
Bernhard Heim and Markus Neuhauser
Department of Mathematics and Science
Faculty of Science
German University of Technology in Oman (GUtech)
PO Box 1816
Athaibah PC 130
Sultanate of Oman
Fourier coefficients of powers of the Dedekind eta function can be
studied by polynomials introduced by M. Newman. We generalize the
defining recurrence relations in this paper. From this we derive new
families of polynomials, which approximate these polynomials from
below and above. Although these families are recursively defined, we
are able to determine explicit closed formulas for both approximating
polynomials. (For the original polynomials closed formulas are not yet
known.) Furthermore, we obtain that both approximating families and the
coefficients involved are log-concave and unimodal.
Full version: pdf,
(Concerned with sequences
Received March 21 2018; revised version received January 3 2019.
Published in Journal of Integer Sequences,
January 6 2019.
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