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q-Legendre based Gould–Hopper polynomials and q-operational methods

The generalization of the monomiality principle for q-special polynomials has just been explained and demonstrated. This extension is used to study the monomiality features of the number of q-special polynomials, such as q-Appell polynomials, q- Gould–Hopper polynomials, two variables q-Hermite, q-Laguerre and q-Legendre polynomials. Additionally, several kinds of hybrid q-special polynomials and their monomiality features are studied, such as two-variable q-Laguerre-Appell polynomials, two-v...

1h-Appell versions of U-Bernoulli and U-Euler polynomials: properties, zero distribution patterns, and the monomiality principle

This paper explores the properties, generating functions, recurrence relations, and summation formulas of a novel class of polynomials, referred to as h-type U-Bernoulli and h-type U-Euler polynomials.We delve into the characterization of these polynomials, including the monomiality principle, and derive the corresponding derivative and multiplicative operators. Additionally, we provide computational values in tables and visually appealing representations of the zeros of these polyn...

Some Hermite-Hadamard Type Integral Inequalities and Their Applications via the Modified Riemann-Liouville Fractional Integral Operator

The aim of this manuscript is to introduce a novel form of H-H inequality via ψ-RLFIO for preinvex functions. By employing this approach, we construct a new lemma. In addition, based on this newly derived fractional identity, some new estimation of fractional H-H inequality involving m-preinvex via ψ-RLFIO is investigated. Further, we add some mean-type applications.

Some novel results on Boubaker polynomials leading to an efficient orthogonalization

The orthogonal polynomials have been recognized in literature due to their compatibility in providing robust and accurate solutions of different nonlinear, singular, and complex problems in science and engineering. The Boubaker polynomial (BPs) and its variants to date have been at galore in the recent literature in this context. Although exhaustive applications of the BPs and its variants have been performed, systematic orthogonalization of the polynomials is still a persistent problem. In o...

Stereohoax: a multilingual corpus of racial hoaxes and social media reactions annotated for stereotypes

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