Results 21 to 30 of about 214 (120)
Quasi‐definiteness of generalized Uvarov transforms of moment functionals
Journal of Applied Mathematics, Volume 1, Issue 2, Page 69-90, 2001., 2001 When σ is a quasi‐definite moment functional with the monic orthogonal polynomial system {P n (x)}n=0∞, we consider a point masses perturbation τ of σ given by τ:=σ+λΣl=1 mΣk=0 ml((−1)kulk/k!)δ (k)(x − c l), where λ, ulk, and cl are constants with ci ≠ cj for i ≠ j. That is, τ is a generalized Uvarov transform of σ satisfying A(x) τ = A(x) σ, where A(x)
D. H. Kim, K. H. Kwon
wiley +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 +2 more
wiley +1 more source
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
wiley +1 more source
Hermite Series with Polar Singularities [PDF]
, 2012 MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are ...
Boychev, Georgi S.
core
Orthogonality of linear combinations of two orthogonal polynomial sequences [PDF]
, 2001 14 pages, no figures.-- MSC2000 code: 33C45.MR#: MR1865881 (2002j:33009)Zbl#: Zbl 0990.42007We find necessary and sufficient conditions for some linear combinations of two sequences of orthogonal polynomials to be again orthogonal.The first author (K.H.K.
Marcellán, Francisco +3 more
core +1 more source
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
wiley +1 more source
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
wiley +1 more source
Equiconvergence and equisummability of Jacobi series [PDF]
, 2011 2010 Mathematics Subject Classification: 33C45, 40G05.In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi ...
Boychev, Georgi
core
Degenerate Hermite poly-Bernoulli numbers and polynomials with q-parameter
, 2020 In this paper, we introduce a new class of degenerate Hermite polyBernoulli polynomials with q-parameter and give some identities of these polynomials related to the Stirling numbers of the second kind.
KHAN, Idrees A. +2 more
core +1 more source
Zeros of Jacobi-Sobolev orthogonal polynomials [PDF]
, 2003 10 pages, no figures.-- MSC2000 codes: 33C45.MR#: MR2027148 (2004m:33017)Zbl#: Zbl pre05376428We investigate zeros of Jacobi-Sobolev orthogonal polynomials with respect to $$\multline \langle f, g\rangle = \int_{-1}^1 f(x)g(x)(1-x)^{ \alpha }(1+x)^{\beta}
Yoon, G. J. +3 more
core +2 more sources