Results 61 to 70 of about 1,802,704 (118)
Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials
Studies in Applied Mathematics, Volume 152, Issue 1, Page 453-507, January 2024.Abstract In this paper, rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalized Laguerre polynomials, which are the main subject of this paper, and the other in terms of the generalized Umemura polynomials. Both the generalized
Peter A. Clarkson, Clare Dunning
wiley +1 more source
A New Generalization of Legendre-Based Appell Polynomials with Two Parameters and Their Applications
AxiomsIn the present work, we introduce and study a new two-parameter generalization of Legendre-based Appell polynomials, defined through an explicit representation that unifies classical Legendre structures with the Appell polynomial framework. Starting from
Ghaliah Alhamzi +4 more
doaj +1 more source
Several Structural Properties and Characterisations of Affine Gould–Hopper-Based Appell Polynomials
MathematicsIn this paper, we introduce and systematically study a new two-parameter family of affine (q,η)-Gould–Hopper-based Appell polynomials. These polynomials arise by fusing the affine (q,η)-exponential Gould–Hopper kernel with an invertible Appell multiplier.
Lateef Ahmad Wani +3 more
doaj +1 more source
MathematicsThis paper develops a two-variable truncated-exponential-based Hahn–Appell polynomial family of order r in quantum q-calculus, generated by A(t)(1−ηtr)−1eqwt(ζt), where A(t) is a normalized determining function and eqwt denotes the Hahn-type q ...
Waseem Ahmad Khan +3 more
doaj +1 more source
Hahn-Appell polynomials and their d-orthogonality
, 2019 Recently, parametric (q,)-exponential functions were defined in [4]. In the present paper, we obtain non-parametric Hahn exponential functions by using the characteristic properties of the usual discrete and q-exponential functions.
Varma, Serhan +2 more
core +1 more source
Some results on q-Hermite based hybrid polynomials [PDF]
, 2018 In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Euler polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived
Riyasat, Mumtaz, Khan, Subuhi
core +1 more source
Combinatorial identities for Appell polynomials [PDF]
, 2018 Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, Norlund ...
Emanuele Munarini, E. Munarini
core +1 more source
Appell polynomials as values of special functions [PDF]
, 2018 We show that there is a large class of Appell sequences {Pn(x)}n=0 ∞ for which there is a function F(s,x), entire in s for fixed x with Rex>0 and satisfying F(−n,x)=Pn(x) for n=0,1,2,….
Navas, L.M. [0000-0002-5742-8679] +7 more
core +1 more source
Adjoint Appell-Euler and First Kind Appell-Bernoulli Polynomials [PDF]
, 2019 The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials.
P. Natalini +3 more
core +1 more source
Deformed Bivariate $q$-Appell Polynomials
In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous polynomials. Next, we give some of their characterizations and algebraic structure.
openaire +2 more sources