Results 81 to 90 of about 700 (183)

On a class of generalized Laguerre's polynomials [PDF]

Časopis pro pěstování matematiky, 1988
This paper deals with polynomials \(L_ n(x)\) orthonormal with respect to the weight function \(| x|^{2\alpha}(b+x)^{\beta}e^{-x}\) on \((a,+\infty)\), \(a\leq 0\), \(\alpha >0\), \(\beta >0\) and \(b+a>0\). The author uses techniques already known to \textit{J. A. Shohat} [Duke Math. J. 5, 401-417 (1939; Zbl 0021.30802)] to show that the coefficients \
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New Laguerre-polynomials’ generating functions derived by virtue of operator Hermite-polynomial method and entangled state representation

AIP Advances
In this paper, we derive two new generating functions of Laguerre-polynomials, which look like the negative binomial theorem for the Laguerre function Lnx, by adopting the bi-partite entangled state representation and the operator-Hermite-polynomial HnX ...
Ke Zhang, Hong-Yi Fan
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The relativistic Laguerre polynomials

Rendiconti di Matematica e delle Sue Applicazioni, 1996
The main topic, in the opinion of the reviewer, is found in the last part of the recent paper: the polynomials considered here are not new, as the author calls them, they are special cases of the well known Jacobi polynomials, and consequently all properties derived in the paper (representation by hypergeometric functions, explicit polynomial ...
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Equioscillatory property of the Laguerre polynomials

Journal of Approximation Theory, 2010
\(L^{(\alpha)}_k\) is the orthonormal Laguerre polynomial of degree \(k\) and \(d_m\), \(d_M\) are some approximations for the extreme zeros. The authors show that the function \[ ((x- d_m)(x- d_M))^{1/4} x^{\alpha/2} e^{-{x\over 2}}L^{(\alpha)}_k(x) \] is almost equi-oscilating with the amplitude \(\sqrt{{2\over\pi}}\) provided \(k\) and \(\alpha ...
Ilia Krasikov, Alexander Zarkh
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Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Mathematics
We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials.
Paolo Emilio Ricci, Rekha Srivastava, Diego Caratelli   +2 more
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

Mathematics, 2019
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim, Dmitry V. Dolgy, Dojin Kim, Taekyun Kim   +3 more
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Integral representations for the product of certain polynomials of two variables

Ain Shams Engineering Journal, 2013
The main object of this paper is to investigate several integral representations for the product of two polynomials of two variables, e.g. Laguerre, Jacobi, Generalized Bessel, Generalized Rice, Krawtchouk, Meixner, Gottlieb and Poisson–Charlier ...
Mumtaz Ahmad Khan, Abdul Hakim Khan, Sayed Mohammad Abbas   +2 more
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An efficient numerical method for fractional order nonlinear two-point boundary value problem occurring in chemical reactor theory

Alexandria Engineering Journal
This paper is focused on computing an approximate numerical solution of the strongly nonlinear multi-order fractional version (SNMOFV) of a BVP that appears in the theory of chemical reactors.
Devendra Kumar, Hunney Nama, Dumitru Baleanu   +2 more
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Multi-variable Gould-Hopper and Laguerre polynomials

Le Matematiche, 2007
The monomiality principle was introduced by G. Dattoli, in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials.
Caterina Cassisa, Paolo E. Ricci
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Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type

Symmetry, Integrability and Geometry: Methods and Applications, 2012
We introduce and study natural generalisations of the Hermite and Laguerre polynomials in the ring of symmetric functions as eigenfunctions of infinite-dimensional analogues of partial differential operators of Calogero-Moser-Sutherland (CMS) type.
Patrick Desrosiers, Martin Hallnäs
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