Abstract
The recursion relationship: is satisfied by all monic orthogonal polynomials in regard to an arbitrary Freud‐type weight function. In current paper, one focuses on the weight function to analyze its relative and . Through above equation and orthogonality, we find that satisfy the first discrete Painlevé equation I Hierarchy and a high‐order differential‐difference equation, respectively. Then, we find that the asymptotic value of is settled by Coulomb fluid. Additionally, we talk about with , including approximation for and , and bounds for as are settled.
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