Advancements in $ q $-Hermite-Appell polynomials: a three-dimensional exploration
Mohra Zayed, Shahid Ahmad Wani, William Ramírez, Clemente Cesarano
Abstract
<p>In this research, we leverage various $ q $-calculus identities to introduce the notion of $ q $-Hermite-Appell polynomials involving three variables, elucidating their formalism. We delve into numerous properties and unveil novel findings regarding these $ q $-Hermite-Appell polynomials, encompassing their generating function, series representation, summation equations, recurrence relations, $ q $-differential formula, and operational principles. Our investigation sheds light on the intricate nature of these polynomials, elucidating their behavior and facilitating deeper understanding within the realm of $ q $-calculus.</p>
Topics & Concepts
Hermite polynomialsDifference polynomialsMathematicsOrthogonal polynomialsPure mathematicsAlgebra over a fieldAdvanced Mathematical IdentitiesMathematical functions and polynomialsAnalytic Number Theory Research