Mixed-Type Hypergeometric Bernoulli-Gegenbauer Polynomials

Article Mathematics

GENERALIZED MIXED TYPE BERNOULLI-GEGENBAUER POLYNOMIALS

Yamilet Quintana

Summary: This paper discusses the algebraic and analytic properties of the generalized mixed type Bernoulli-Gegenbauer polynomials of order alpha > -21. These special polynomials, obtained using the generating function method, represent an interesting combination of generalized Bernoulli polynomials and Gegenbauer polynomials.

KRAGUJEVAC JOURNAL OF MATHEMATICS (2023)

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Article Multidisciplinary Sciences

Lagrange-Based Hypergeometric Bernoulli Polynomials

Sahar Albosaily et al.

Summary: Special polynomials play a significant role in mathematics, engineering, and theoretical physics, particularly in the context of differential equations. This paper introduces a family of Lagrange-based hypergeometric Bernoulli polynomials and discusses their algebraic and differential properties, as well as related formulas. Furthermore, future research could explore potential applications of these polynomials in the mentioned disciplines.

SYMMETRY-BASEL (2022)

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Article Mathematics

Discrete Hypergeometric Legendre Polynomials

Tom Cuchta et al.

Summary: This study investigates a discrete analog of Legendre polynomials defined by discrete hypergeometric series. The resulting polynomials exhibit qualitatively similar properties to classical Legendre polynomials, and their difference equations, recurrence relations, and generating function are derived.

MATHEMATICS (2021)

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Article Mathematics, Applied