Results 41 to 50 of about 1,268 (75)

Efficient scheme for a category of variable-order optimal control problems based on the sixth-kind Chebyshev polynomials

Demonstratio Mathematica
The main goal of the present study is to introduce an operational collocation scheme based on sixth-kind Chebyshev polynomials (SCPs) to solve a category of optimal control problems involving a variable-order dynamical system (VODS). To achieve this goal,
Sadri Khadijeh, Hosseini Kamyar, Salahshour Soheil, Baleanu Dumitru, Ahmadian Ali, Park Choonkil   +5 more
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Integral Representations of Functional Series with Members Containing Jacobi Polynomials [PDF]

, 2012
MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi ...
Jankov, Dragana, Pogany, Tibor K.
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Generalized Chebyshev polynomials of the second kind

, 2015
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis.
AlQudah, Mohammad A.
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A new perspective on generalized Laguerre polynomials

Demonstratio Mathematica
This article introduces two-variable polynomials constructed with generalized Laguerre polynomials. The study focuses on deriving generating function relationships, establishing closed-form summation formulas, and proving a symmetry identity for the ...
Erkuş-Duman Esra
doaj   +1 more source

Eulerian polynomials as moments, via exponential Riordan arrays [PDF]

, 2011
Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials, which we ...
Barry, Paul
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Convexity of the zeros of some orthogonal polynomials and related functions

, 2008
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions ...
Ahmed, Brezinski, Deaño, Deaño, Ferenc Tookos, Gori, Hahn, Hille, Kalamajska, Kerstin Jordaan, Laforgia, Lorch, Makai, Muldoon, Redheffer, Sturm, Szegő, Szegő   +17 more
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Meta algebras and biorthogonal rational functions: The Hahn case

Forum of Mathematics, Sigma
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated meta Hahn algebra and its finite-dimensional representations.
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov   +2 more
doaj   +1 more source

A Dunkl Analogue of Operators Including Two-variable Hermite polynomials

, 2017
The aim of this paper is to introduce a Dunkl generalization of the operators including two variable Hermite polynomials which are defined by Krech [14](Krech, G.
Aktaş, Rabia, Taşdelen, Fatma, Çekim, Bayram   +2 more
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An integral formula for L^2-eigenfunctions of a fourth order Bessel-type differential operator

, 2010
We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions.
Erdélyi A., Gradshteyn I. S., Jan Möllers, Toshiyuki Kobayashi   +3 more
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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