Results 31 to 40 of about 1,331 (75)
Demonstratio MathematicaThe 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 +5 more
doaj +1 more source
in "Advances in Combinatorics", Waterloo Workshop in Computer
Algebra W80, Springer (2013), 287--293, 2012 We explain the use and set grounds about applicability of algebraic transformations of arithmetic hypergeometric series for proving Ramanujan's formulae for $1/\pi$ and their generalisations.
arxiv +1 more source
Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequences [PDF]
arXiv, 2019 We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships between the moments of these orthogonal polynomials, the moments of the defining Laurent biorthogonal polynomials, and the expansions of $T$-fractions. Closed form expressions
arxiv
Remarks on orthogonal polynomials with respect to varying measures and related problems
, 1992 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 255-258, 1993.
Xin Li
wiley +1 more source
On the orthogonality and convolution orthogonality via the Kontorovich-Lebedev transform [PDF]
arXiv, 2019 Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral representations, orthogonality relations and explicit expressions are established.
arxiv
Bivariate q-Laguerre–Appell polynomials and their applications
Applied Mathematics in Science and EngineeringRecently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered.
Mohammed Fadel +3 more
doaj +1 more source
Fisher information of orthogonal polynomials I [PDF]
arXiv, 2007 Following the lead of J. Dehesa and his collaborators, we compute the Fisher information of the Meixner-Pollaczek, Meixner, Krawtchouk and Charlier polynomials.
arxiv
Polynomial solutions of nonlinear integral equations [PDF]
, 2008 We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.
arxiv +1 more source
Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials
Open MathematicsThis study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials.
Wani Shahid Ahmad +2 more
doaj +1 more source
An urn model associated with the Jacobi polynomials [PDF]
arXiv, 2009 We consider an urn model leading to a random walk that can be solved explicitly in terms of the well known Jacobi polynomials.
arxiv