Results 21 to 30 of about 2,744 (114)
The Hermite polynomials and the Bessel functions from a general point of view
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 57, Page 3633-3642, 2003., 2003 We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show that they satisfy differential‐difference equations which are isospectral to those of the ordinary case.
G. Dattoli +2 more
wiley +1 more source
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
wiley +1 more source
Zeros of linear combinations of Laguerre polynomials from different sequences [PDF]
, 2008 We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely $R_n=L_n^{\alpha}+aL_{n}^{\alpha'}$ and $S_n=L_n^{\alpha}+bL_{n-1}^{\alpha'}$. Proofs and numerical counterexamples
Brezinski +9 more
core +2 more sources
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
Some results on hybrid relatives of the Sheffer polynomials via operational rules
Miskolc Mathematical Notes, 2019 The intended objective of this paper is to introduce a new class of polynomials, namely the extended Laguerre-Gould-Hopper-Sheffer polynomials. The generating function and operational rule are derived by making use of integral transform.
Mahvish Ali, Tabinda Nahid, Subuhi Khan
semanticscholar +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
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
Discrete orthogonality of hypergeometric polynomial sequences on linear and quadratic lattices [PDF]
arXiv, 2022 We present a method to obtain weight functions associated with linear and quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional of the orthogonal polynomial sequences in the Askey scheme, with the exception of the Jacobi, Bessel, Laguerre, and Hermite polynomials.
arxiv
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Koornwinder, Tom H.
core +6 more sources
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
wiley +1 more source