Real-rootedness of quartic Jensen polynomials associated with pod ( n )

Let [Formula: see text] denote the number of partitions of [Formula: see text] into distinct odd parts. In this paper, we prove that the quartic Jensen polynomial associated with [Formula: see text]: [Formula: see text] has four distinct real roots for all [Formula: see text]. To achieve this, we establish several inequalities for [Formula: see text] by utilizing its arbitrary-precision error estimates. Furthermore, we confirm the positivity of a class of third-order determinants with entries given by [Formula: see text], which can be viewed as a generalization of previous results on third-order Toeplitz matrices related to [Formula: see text].