67 research outputs found
The -log-convexity of Domb's polynomials
In this paper, we prove the -log-convexity of Domb's polynomials, which
was conjectured by Sun in the study of Ramanujan-Sato type series for powers of
. As a result, we obtain the log-convexity of Domb's numbers. Our proof is
based on the -log-convexity of Narayana polynomials of type and a
criterion for determining -log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273
On the -log-convexity conjecture of Sun
In his study of Ramanujan-Sato type series for , Sun introduced a
sequence of polynomials as given by
and he conjectured that the polynomials are -log-convex. By
imitating a result of Liu and Wang on generating new -log-convex sequences
of polynomials from old ones, we obtain a sufficient condition for determining
the -log-convexity of self-reciprocal polynomials. Based on this criterion,
we then give an affirmative answer to Sun's conjecture
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