Results 41 to 50 of about 233,365 (231)

Zeros of some difference polynomials [PDF]

Advances in Difference Equations, 2013
In this paper, we study zeros of some difference polynomials in f (z) and their shifts, where f (z) is a finite order meromorphic function having deficient value ∞. These results improve previous findings.
Zong-Xuan Chen, Shuangting Lan
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Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials

Journal of Symbolic Computation, 2021
This article addresses the problem of computing an upper bound of the degree d of a polynomial solution P(x) of an algebraic difference equation of the form G(x)(P(x−τ1),…,P(x−τs))+G0(x)=0 when such P(x) with the coefficients in a field K of characteristic zero exists and where G is a non-linear s-variable polynomial with coefficients in K[x] and G0 is
Olha Shkaravska, Olha Shkaravska, Marko van Eekelen, Marko van Eekelen   +3 more
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Sequences of twice-iterated Δw-Gould–Hopper Appell polynomials

Journal of Taibah University for Science
In this paper, we introduce general sequence of twice-iterated [Formula: see text]-(degenerate) Gould–Hopper Appell polynomials (TI-DGHAP) via discrete [Formula: see text]-Gould–Hopper Appell convolution. We obtain some of their characteristic properties
Neslihan Biricik, Bayram Çekim, Mehmet Ali Özarslan   +2 more
doaj   +1 more source

A note on generalized q-difference equations for general Al-Salam–Carlitz polynomials

Advances in Difference Equations, 2020
In this paper, we deduce the generalized q-difference equations for general Al-Salam–Carlitz polynomials and generalize Arjika’s recent results (Arjika in J. Differ. Equ. Appl. 26:987–999, 2020).
Jian Cao, Binbin Xu, Sama Arjika
doaj   +1 more source

On factorization of q-difference equation for continuous q-Hermite polynomials

, 2007
We argue that a customary q-difference equation for the continuous q-Hermite polynomials H_n(x|q) can be written in the factorized form as (D_q^2 - 1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference operator.
A U Klimyk, Akhiezer N I, Andrews G E, Askey R, Biedenharn L C, Gasper G, Ismail M E H, Koekoek R Swarttouw R F, Koornwinder T H, Kulish P P, Landau L D, M N Atakishiyev, Macfarlane A J, Nikiforov A F, Samsonov B F   +14 more
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A generalized Macdonald operator

, 2010
We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems.
Baratta, Bourbaki, E. Emsiz, J. F. van Diejen, Komori, Lassalle, Lassalle, Macdonald, Macdonald, Stembridge, Stembridge, van Diejen, van Diejen, van Diejen, van Diejen   +14 more
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Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

Journal of Advanced Research, 2010
Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
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Lie-algebraic discretization of differential equations

, 1995
A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based approach, (quasi)-
Smirnov, Yuri, Turbiner, Alexander
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Value Distribution of Certain Type of Difference Polynomials

Abstract and Applied Analysis, 2014
We investigate the value distribution of difference product f(z)n∑i=1k‍aif(z+ci), for n≥2 and n=1, respectively, where f(z) is a transcendental entire function of finite order and ai,ci are constants satisfying ∑i=1k‍aif(z+ci)≢0.
Nan Li, Lianzhong Yang
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Properties of some difference polynomials

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2013
In this article, we investigate some properties of some difference polynomials. The results in this article improve some theorems of Liu and Laine. Several examples are provided to show that our results are best possible.
Liu, Yong, Yi, Hong-Xun
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