Lagrange-Based Hypergeometric Bernoulli Polynomials

Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this paper, we introduce the family of the Lagrange-based...

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Published inSymmetry (Basel) Vol. 14; no. 6; p. 1125
Main Authors Albosaily, Sahar, Quintana, Yamilet, Iqbal, Azhar, Khan, Waseem A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2022
Subjects
Algebra
Bernoulli Hypothesis
Combinatorial analysis
Differential equations
Mathematical analysis
Polynomials
Theoretical physics
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Summary:Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this paper, we introduce the family of the Lagrange-based hypergeometric Bernoulli polynomials via the generating function method. We state some algebraic and differential properties for this family of extensions of the Lagrange-based Bernoulli polynomials, as well as a matrix-inversion formula involving these polynomials. Moreover, a generating relation involving the Stirling numbers of the second kind was derived. In fact, future investigations in this subject could be addressed for the potential applications of these polynomials in the aforementioned disciplines.
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content type line 14
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14061125