Results 41 to 50 of about 1,259 (74)

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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Lacunary generating functions of Hermite polynomials and symbolic methods [PDF]

, 2015
We employ an umbral formalism to reformulate the theory of Hermite polynomials and the derivation of the associated lacunary generating ...
D. Babusci, G. Dattoli, GERMANO, Bruna, MARTINELLI, Maria Renata, P. E. Ricci   +4 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
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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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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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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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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
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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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Dual -1 Hahn polynomials and perfect state transfer

, 2011
We find all the $XX$ spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials $R_n(x; \alpha,\beta,N)$. For $N$ odd we recover a model that had already been identified while for $N$ even, we obtain a new system ...
AKay, Alexei Zhedanov, Luc Vinet, LVinet, NStoilova, RKoekoek, Rosenblum M, Shi T, STsujimoto, STsujimoto, STsujimoto, Szegó G   +11 more
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A Note on a Classical Generating Function for the Jacobi Polynomials [PDF]

, 2005
Mathematics Subject Classification: 33C45.A more general form for a classical generating function for the Jacobi polynomials is given.* Partially supported by Project MM 1305 - National Science Fund, Bulgarian Ministry of Educ ...
Rusev, Peter
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