Bibliographic Information: G¨uldo˘gan Lekesiz, E., C¸ekim, B., & ¨Ozarslan, M. A. (2024). Finite bivariate biorthogonal N-Konhauser polynomials. arXiv preprint arXiv:2410.18056v1.
Research Objective: To define and investigate a new set of finite bivariate biorthogonal polynomials, termed "finite bivariate biorthogonal N-Konhauser polynomials" (fNKp), and to explore their properties and applications.
Methodology: The authors utilize mathematical derivation and analysis, building upon existing theory of orthogonal polynomials, particularly Konhauser polynomials and generalized Laguerre-Konhauser polynomials. They derive generating functions, recurrence relations, and partial differential equations satisfied by these new polynomials.
Key Findings:
Main Conclusions: The introduction of fNKp enriches the family of orthogonal polynomials and provides a new tool for mathematical modeling and analysis in various fields. The established connections to other polynomial families and the derived properties highlight their potential in areas like fractional calculus, integral transforms, and solving specific types of differential equations.
Significance: This research significantly contributes to the field of orthogonal polynomials by introducing a novel set of biorthogonal polynomials and thoroughly investigating their properties. The findings have implications for various mathematical applications, including approximation theory, numerical analysis, and solving problems in physics and engineering.
Limitations and Future Research: The paper primarily focuses on the theoretical aspects of fNKp. Further research could explore:
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