Journal of Integer Sequences, Vol. 22 (2019), Article 19.1.5

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,    dvi,    ps,    latex    

(Concerned with sequences A000041 A000594 A089231 A322970.)

Received March 21 2018; revised version received January 3 2019. Published in Journal of Integer Sequences, January 6 2019.

Return to Journal of Integer Sequences home page