Results 81 to 90 of about 18,610 (207)

A Lucas Operational Matrix Method for Solving Nonlinear Fractional Two‐Dimensional Partial Volterra Integral Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper introduces a new numerical method for solving a class of two‐dimensional fractional partial Volterra integral equations (2DFPVIEs). Our approach uses Lucas polynomials (LPs) to construct operational matrices (OMs) that effectively transform the complex fractional‐order equations into a more manageable system of algebraic equations.
S. S. Gholami, A. Ebadian, A. A. Khajehnasiri, Kareem T. Elgindy, Birendra Nath Mandal   +4 more
wiley   +1 more source

The telephone polynomials: An Appell-type orthogonal polynomials connecting Hermite–Laguerre polynomials

Nuclear Physics B
This article investigates a new Appell-type sequence, the telephone polynomials, which extend the classical telephone (involution) numbers. We present their fundamental algebraic properties, structural characterizations, and diverse interconnections with
Kalika Prasad, Munesh Kumari
doaj   +1 more source

A method for fractional Volterra integro-differential equations by Laguerre polynomials

Advances in Difference Equations, 2018
The main purpose of this study is to present an approximation method based on the Laguerre polynomials for fractional linear Volterra integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic
Dilek Varol Bayram, Ayşegül Daşcıoğlu   +1 more
doaj   +1 more source

Series Solution to a Fuchsian‐Type Differential Equation in Terms of Orthogonal Polynomials

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we study a thirteen‐parameter Fuchsian‐type second‐order linear differential equation that involves five regular singularities. By employing a tridiagonal representation technique, we formulate four cases under which the series solutions of the equation are obtained in terms of Jacobi polynomials.
Saiful Rahman Mondal, Pratap Narayan Pathak, Smritijit Sen   +2 more
wiley   +1 more source

A note on pseudo Jacobi polynomials

Ain Shams Engineering Journal, 2013
The present paper is a study of pseudo-Jacobi polynomials which have been defined on the pattern of Shively’s pseudo-Laguerre polynomials. The paper contains generating functions, Rodrigues formula, recurrence relations and expansion of pseudo-Jacobi ...
Mumtaz Ahmad Khan, Abdul Hakim Khan, Sayed Mohammad Abbas   +2 more
doaj   +1 more source

Laguerre polynomial expansions

Journal of Computational and Applied Mathematics, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

LAGUERRE AND MEIXNER POLYNOMIALS IN DUALITY [PDF]

Glasgow Mathematical Journal, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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, Waleed K. Mohammed, Guotao Wang   +2 more
wiley   +1 more source

Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics

Symmetry, Integrability and Geometry: Methods and Applications, 2009
New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the corresponding conventional superpotential and on the ...
Christiane Quesne
doaj   +1 more source

Non-Linear Observer Design with Laguerre Polynomials. [PDF]

Entropy (Basel), 2022
Trigka M, Dritsas E.
europepmc   +1 more source