In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial f on a basic closed set K ⊂ R. The interest in such identities originates not least from their importance in polynomial optimization. The majority of the important results requires the archimedean condition, which implies that K has to be compact....

Building on the works of S. Bochner equivalence modular relation with functional equation associated to Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained new equivalences between some arithmetical identities. Sister Ann M. Heath considered in Hawkins Knopp context showed its two identities entire cusp integrals involving rational period functions for full group. In this paper we u...

We prove a new polynomial refinement of the Capparelli's identities. Using special case Bailey's lemma we many infinite families sum-product identities that root from our finite analogues also discuss q ↦ 1 / duality transformation base and some related partition theoretic relations.

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them techniques. By leveraging properties of Pascal functionals and Wronskian matrices, derive several identities for these polynomials, including recurrence relations. It is highlighted that identities, acquired via techniques, are distinct from the ones obta...