Results 21 to 30 of about 80 (77)
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 673-689, 2000., 2000 We give explicitly the recurrence coefficients of a nonsymmetric semi‐classical sequence of polynomials of class s = 1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an arbitrary parameter with ℜ(1 − μ) > 0 in such a way that for μ = 0 one has the well‐known Jacobi ...
Mohamed Jalel Atia
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study introduces a novel family of hybrid Kantorovich‐type operators for the Baskakov–Schurer–Stancu class, integrated with a shape parameter α ∈ [0, 1]. We establish fundamental estimates and evaluate both the rate of convergence and the order of approximation utilizing the Korovkin theorem and the modulus of smoothness.
Md. Nasiruzzaman +5 more
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On 2‐orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 29-48, 1999., 1999 Let be a sequence of 2‐orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let be the sequence of polynomials defined by . When is, also, 2‐orthogonal, is called “classical” (in the sense of having the Hahn property). In this case, both and satisfy a third‐order recurrence relation (see below).
Khalfa Douak
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On Laguerre-Sobolev matrix orthogonal polynomials
Open MathematicsIn this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson +2 more
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A Family of Hybrid Functions Generated by the Composition of Bessel and Mittag–Leffler Functions
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we employ a symbolic technique to introduce a new family of Mittag–Leffler–Bessel functions (MLBFs), formed by compositionally combining the classical Bessel functions of the first kind with the three‐parameter Mittag–Leffler function.
Maged G. Bin-Saad +2 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we propose a projection method that utilizes shifted airfoil polynomials to solve systems of weakly singular fractional integro‐differential equations (FIDEs). The proposed approach converts the original system into two linear algebraic systems, facilitating efficient numerical solutions.
Saeed Althubiti, Chang Phang
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Some new forms and properties of Legendre matrix polynomials with two variables
Demonstratio MathematicaThis paper aims to introduce new significant forms of the Legendre matrix polynomials (LMPs) with two variables, and establish matrix differential recurrence relations and matrix partial differential recurrence relations for LMPs with two variables, and ...
Khammash Ghazi S. +3 more
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Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli +3 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The Y‐function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric‐type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y‐function, this study establishes four ...
Engdasew Birhane +2 more
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On the Generalized Class of Multivariable Humbert‐Type Polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The present paper deals with the class of multivariable Humbert polynomials having generalization of some well‐known polynomials like Gegenbauer, Legendre, Chebyshev, Gould, Sinha, Milovanović‐Djordjević, Horadam, Horadam‐Pethe, Pathan and Khan, a class of generalized Humbert polynomials in two variables etc.
B. B. Jaimini +4 more
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