Results 21 to 30 of about 1,268 (75)
On a generalized Jacobi transform
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 371-385, 2002., 2002 In this paper, we study a generalized Jacobi transform and obtain images of certain functions under this transform. Furthermore, we define a Jacobi random variable and derive its moments, distribution function, and characteristic function.
José Sarabia, S. L. Kalla
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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
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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
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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
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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
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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
Characterization of the generalized Chebyshev-type polynomials of first kind
, 2015 Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials.
AlQudah, Mohammad A.
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Turán inequalities for symmetric orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 1-7, 1997., 1997 A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q‐Bessel functions.
Joaquin Bustoz, Mourad E. H. Ismail
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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 +2 more
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A note on monotonicity property of Bessel functions
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 561-566, 1997., 1997 A theorem of Lorch, Muldoon and Szegö states that the sequence is decreasing for α > −1/2, where Jα(t) the Bessel function of the first kind order α and jα,k its kth positive root. This monotonicity property implies Szegö′s inequality , when α ≥ α′ and α′ is the unique solution of .
Stamatis Koumandos
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