Results 31 to 40 of about 45,205 (253)

Bootstrapping and Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Jang Soo Kim, Dennis Stanton
openaire   +3 more sources

The non-symmetric Wilson polynomials are the Bannai–Ito polynomials [PDF]

Proceedings of the American Mathematical Society, 2016
The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and the Bannai-Ito algebra is established.
Luc Vinet, Vincent X. Genest, Alexei Zhedanov   +2 more
openaire   +3 more sources

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
doaj   +1 more source

A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the
Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng   +3 more
doaj   +1 more source

Analysing Effects of Birth Order on Intelligence, Educational Attainment, Big Five, and Risk Aversion in an Indonesian Sample

European Journal of Personality, EarlyView., 2020
Abstract Few studies have examined birth order effects on personality in countries that are not Western, educated, industrialized, rich, and democratic (WEIRD). However, theories have generally suggested that interculturally universal family dynamics are the mechanism behind birth order effects, and prominent theories such as resource dilution would ...
Laura J. Botzet, Julia M. Rohrer, Ruben C. Arslan   +2 more
wiley   +1 more source

Bispectrality of Multivariable Racah–Wilson Polynomials [PDF]

Constructive Approximation, 2009
minor ...
Plamen Iliev, Jeffrey S. Geronimo
openaire   +4 more sources

The colored Jones polynomials as vortex partition functions

Journal of High Energy Physics, 2021
We construct 3D N $$ \mathcal{N} $$ = 2 abelian gauge theories on S $$ \mathbbm{S} $$ 2 × S $$ \mathbbm{S} $$ 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored ...
Masahide Manabe, Seiji Terashima, Yuji Terashima   +2 more
doaj   +1 more source

Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]

, 2013
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
core   +3 more sources

Non-symmetric Jacobi and Wilson type polynomials [PDF]

International Mathematics Research Notices, 2005
Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure $|c(\lam)|^{-2}d\lam$.
Lizhong Peng, Genkai Zhang
openalex   +5 more sources

Expansions in the Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
Abstract We give a general expansion formula of functions in the Askey–Wilson polynomials and using Askey–Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey–Wilson type, which are not necessarily orthogonal.
Mourad E. H. Ismail, Mourad E. H. Ismail, Dennis Stanton   +2 more
openaire   +3 more sources