Positivity certificates for P-recursive sequences

We consider sequences which satisfy a linear recurrence equation Ly = 0 with polynomial coefficients. A criterion, i.e., a necessary and sufficient condition is proposed for validity of the discrete Newton-Leibniz formula when a primitive (an indefinite ...

In this paper, we present some criteria for the 2-$q$-log-convexity and 3-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of a certain infinite triangular array $[A_{n,k}(q)]_{n,k\geq0}$ of polynomials in $q$ with ...

We consider the higher order Turán inequality and higher order log-concavity for sequences { a n } n ≥ 0 such that a n − 1 a n + 1 a n 2 = 1 + ∑ i = 1 m r i ( log ⁡ n ) n α i + o ( 1 n β ) , ...