Results 31 to 40 of about 3,034 (119)

Generalized and mixed type Gegenbauer polynomials

Journal of Mathematical Analysis and Applications, 2012
Using the integral representation method and the monomiality principle (see e.g.[\textit{G. Dattoli}, Advanced special functions and applications. Proceedings of the workshop, Melfi, Italy, May 9-12, 1999. Rome: Aracne Editrice. Proc. Melfi Sch. Adv. Top. Math. Phys.
Khan, Subuhi, Al-Gonah, Ahmed Ali, Yasmin, Ghazala   +2 more
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A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

Axioms, 2023
Three subclasses of analytic and bi-univalent functions are introduced through the use of q−Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads
Ala Amourah, Abdullah Alsoboh, Osama Ogilat, Gharib Mousa Gharib, Rania Saadeh, Maha Al Soudi   +5 more
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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

International Journal of Mathematics and Mathematical Sciences, 2004
A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx, Nele De Schepper, Frank Sommen   +2 more
doaj   +1 more source

Criterion for polynomial solutions to a class of linear differential equation of second order [PDF]

, 2006
We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n ...
Al-Salam W A, Barakat T, Barakat T, Bayrak O, Chihara T S, Ciftci H, Ciftci H, Erdélyi A, Fernández M F, Grünbaum F A, Hakan Ciftci, Littlejohn L L, Nasser Saad, Richard L Hall, Saad N, Turbiner A   +15 more
core   +1 more source

On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

International Journal of Mathematics and Mathematical Sciences, 2009
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2.
Tian-Xiao He, Peter J.-S. Shiue
doaj   +1 more source

Explicit solution of the quantum three-body Calogero-Sutherland model [PDF]

, 1998
Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a ...
A M Perelomov, Calogero F, E Ragoucy, Harish-Chandra, Harish-Chandra, Helgason S, Herz C, Jack H, James A, Koornwinder T, Koornwinder T, Koornwinder T, Lassalle M, Macdonald I G, Olshanetsky M A, Olshanetsky M A, Patera J, Perelomov A M, Perelomov A M, Ph Zaugg, Prati M-C, Sekiguchi J, Stanley R P, Sutherland B, Vilenkin N Ja, Vretare L, Vretare L, Weyl H, Weyl H, Weyl H   +29 more
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Dimensional Reduction for Conformal Blocks [PDF]

, 2016
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1 dimensions.
Hogervorst, Matthijs
core   +2 more sources

The affine group and generalized Gegenbauer polynomials

Computers & Mathematics with Applications, 2001
Let \((\xi_1,\xi_2)\) denote a basis of the Lie algebra \(\mathbb{L}\) of the affine group with commutator relation \([\xi_1,\xi_2] =\xi_2\). Representing \(\mathbb{L}\) by the action on polynomials leads to the investigation of operators of the following type: Put \(\xi_1= x\cdot D+\alpha\) (for some constant \(\alpha)\), i.e. \(\xi_1x^n= (n+\alpha) x^
Feinsilver, Ph., Franz, U.
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Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited

Econometrics, 2016
In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory.
M. Shelton Peiris, Manabu Asai
doaj   +1 more source

On generalization of extended Gegenbauer polynomials of two variables

Open Journal of Mathematical Analysis, 2021
Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and ...
Ahmed Ali Al-Gonah, Ahmed Ali Atash
openaire   +1 more source