Abstract
Mohamed Jalel Atia is a mathematician whose research focuses on special functions, hypergeometric series, orthogonal polynomials, transformation identities, and mathematical analysis. His scholarly contributions have advanced the theoretical understanding of generalized mathematical functions and analytical techniques used in pure mathematics. Through publications in peer-reviewed international journals, he has explored extensions of classical identities, polynomial structures, and transformation formulas that support ongoing developments in mathematical research.
Keywords
Mathematics; Hypergeometric Functions; Orthogonal Polynomials; Special Functions; Mathematical Analysis; Transformation Theory; Bessel Polynomials; Mathematical Identities.
Introduction
Mathematics relies on the development of rigorous theoretical frameworks and analytical methods that enable progress across both pure and applied disciplines. Among the specialized areas of modern mathematical research, special functions and orthogonal polynomial theory continue to play important roles in mathematical modeling, computational methods, and theoretical analysis.
Mohamed Jalel Atia has contributed to these fields through research on hypergeometric functions, transformation formulas, polynomial systems, and generalized analytical structures. His work builds upon classical mathematical theories while introducing extensions and refinements that enhance the understanding of complex mathematical relationships.
Academic Background
Mohamed Jalel Atia earned advanced academic qualifications in mathematics from Université de Tunis El Manar and has maintained academic and research affiliations with Université de Gabès and Qassim University. His research activities reflect international collaboration and sustained engagement with theoretical mathematics.
His academic interests are primarily centered on:
Hypergeometric functions and series
Orthogonal polynomial theory
Mathematical analysis
Transformation identities
Special functions
Functional equations
Polynomial linearization methods
Research Contributions
Hypergeometric Functions and Transformation Theory
A major area of Atia’s research concerns hypergeometric functions and their associated transformation formulas. These functions occupy a central position in mathematical analysis due to their applications in differential equations, mathematical physics, and computational mathematics.
His studies have investigated extensions of classical transformation identities and conditions under which generalized transformations may be established. These contributions provide new perspectives on longstanding mathematical problems and support the development of broader analytical frameworks.
Orthogonal Polynomials
Orthogonal polynomial systems are widely used throughout mathematics and applied sciences. Atia has conducted research into generalized orthogonal polynomial structures and associated linear functionals.
His work contributes to understanding the algebraic and analytical properties of polynomial families while extending classical polynomial theories into more generalized settings.
Bessel Polynomial Analysis
Another significant aspect of his research involves Bessel polynomials and their linearization coefficients. Through analytical investigations, he has examined inverse linearization processes and mathematical relationships governing polynomial expansions.
These studies contribute to the broader literature on special functions and polynomial approximation methods.
Positive Definite Linear Functionals
Atia has also explored generalized positive definite linear functionals associated with orthogonal polynomial theory. Such functionals play important roles in approximation theory, functional analysis, and the construction of polynomial systems with desirable mathematical properties.
His research has introduced generalized frameworks that extend classical polynomial constructions and provide new analytical tools for theoretical investigation.
Selected Publications
Reduction for a Terminating Bivariate Hypergeometric Appell Series F1 (II) (2026)
Published in Mathematics, this work investigates reduction formulas associated with terminating bivariate hypergeometric Appell series. The study contributes to the simplification and analysis of special function expressions and provides new mathematical identities relevant to hypergeometric theory.
Extension of Chu–Vandermonde Identity and Quadratic Transformation Conditions (2024)
Published in Axioms, this research extends classical Chu–Vandermonde identities and examines conditions associated with quadratic transformations. The findings contribute to the broader understanding of transformation theory within hypergeometric analysis.
On the Inverse of the Linearization Coefficients of Bessel Polynomials (2024)
Published in Symmetry, this article explores inverse linearization coefficients associated with Bessel polynomials. The study provides analytical results that advance the theoretical understanding of polynomial structures and special function theory.
A Positive Definite Linear Functional of Class s=2: Generalization of Chebyshev Polynomials (2020)
Published in Periodica Mathematica Hungarica, this work investigates generalized positive definite linear functionals and their relationship to Chebyshev polynomial systems. The research expands classical polynomial theory and contributes to the study of orthogonal polynomial structures.
Research Impact
Mohamed Jalel Atia has authored multiple peer-reviewed publications indexed in international scholarly databases. His research contributes to specialized areas of mathematics involving hypergeometric analysis, orthogonal polynomials, and transformation identities.
Theoretical developments arising from his work support ongoing investigations in pure mathematics and provide analytical methods relevant to mathematical modeling, computational techniques, and advanced mathematical research.
Conclusion
Mohamed Jalel Atia's research career reflects sustained contributions to the study of special functions, hypergeometric series, transformation identities, and orthogonal polynomial theory. Through investigations into classical and generalized mathematical structures, he has expanded theoretical knowledge within several specialized domains of mathematics. His publications continue to contribute to the advancement of analytical methods and mathematical understanding in contemporary research.
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