In this paper, we establish a result concerning eigenvector for the product of two operators C and D defined on a Lie algebra of endomorphisms of a vector space. Further, A new method has been devised to define some properties viz. differential recurrence relations and differential equations of 2-variables generalized Hermite matrix polynomials and 2variables matrix Laguerre polynomials to deri...

Abstract Stenger conjectures are claims about the location of eigenvalues matrices whose elements certain integrals involving basic Lagrange interpolating polynomials supported on zeros orthogonal polynomials. In this paper, we show validity extended conjecture for families classical We also restricted Strenger a family Jacobi and generalized Laguerre A connection with -stability collocation Ru...

Laguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form 〈p,q〉S = ∫∞ 0 p(x)q(x)x αe−x dx + λ∫∞ 0 p′(x)q′(x)dμ(x), where α > −1, λ 0, and p,q ∈ P, the linear space of polynomials with real coefficients. If dμ(x) = xαe−x dx, the corresponding sequence of monic orthogonal polynomials {Q n (x)} has been studied by Marcellán et al. (J. Comput. Appl. Math. 71 (1996) 24...

Abstract It is shown that the extensions of exactly-solvable quantum mechanical problems connected with replacement ordinary derivatives by Dunkl ones and classical orthogonal polynomials exceptional can be easily combined. For such a purpose, example oscillator on line considered three different types rationally-extended oscillators are constructed. The corresponding wavefunctions expressed in...

A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the measure |x|γ(1 − x2)1/2dx is derived which is based on a “reversing property” of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalizati...

We consider a modiication of moment functionals for some classical polynomials of a discrete variable by adding a mass point at x = 0. We obtain the resulting orthogonal polynomials, identify them as hypergeometric functions and derive the second order diierence equation which these polynomials satisfy. The corresponding tridiagonal matrices and associated polynomials were also studied. x1 Intr...

In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite Bell-Hermite find representations. We derive some implicit summation formulae symmetric identities for these families special functions by applying the generating functions.

We look for differential equations of the form ∞ ∑ i=0 ci(x)y (x) = 0, where the coefficients {ci(x)} ∞ i=0 are continuous functions on the real line and where {ci(x)} ∞ i=1 are independent of n, for the generalized Jacobi polynomials { P n (x) } ∞ n=0 and for generalized Laguerre polynomials { L n (x) } ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We use a metho...

We look for differential equations of the form ∞ ∑ i=0 ci(x)y (x) = λny(x), where the coefficients {ci(x)} ∞ i=0 do not depend on n, for the generalized Jacobi polynomials { P n (x) } ∞ n=0 found by T.H. Koornwinder in 1984 and for generalized Laguerre polynomials { L n (x) } ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We introduce a method which makes use of co...