Results 31 to 40 of about 122,453 (243)
Exceptional Jacobi polynomials [PDF]
Journal of Approximation Theory, 2019 40 pages, 1 ...
openaire +3 more sources
Multiple little q-Jacobi polynomials [PDF]
, 2004 We introduce two kinds of multiple little q-Jacobi polynomials by imposing orthogonality conditions with respect to r discrete little q-Jacobi measures on the exponential lattice q^k (k=0,1,2,3,...), where 0 < q < 1.
Postelmans, Kelly, Van Assche, Walter
core +4 more sources
Matrix-Valued Little q-Jacobi Polynomials [PDF]
, 2014 Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2x2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their
Aldenhoven, Noud +2 more
core +4 more sources
$-1$ Krall–Jacobi polynomials [PDF]
Methods and Applications of Analysis, 2015 9 ...
Alexei Zhedanov, Guo-Fu Yu, Luc Vinet
openaire +3 more sources
Jacobi Polynomials on the Bernstein Ellipse [PDF]
Journal of Scientific Computing, 2017 In this paper, we are concerned with Jacobi polynomials $P_n^{( , )}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{( , )}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value
Haiyong Wang, Lun Zhang
openaire +2 more sources
Differentiation by integration with Jacobi polynomials
Journal of Computational and Applied Mathematics, 2011 In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join is revisited in the central case where the used integration window is centered. Such method based on Jacobi polynomials was introduced through an algebraic approach and extends the numerical differentiation by ...
Liu, Da-Yan +2 more
openaire +5 more sources
The structure relation for Askey-Wilson polynomials [PDF]
, 2006 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n ...
Koornwinder, Tom H.
core +2 more sources
On the Behaviour of Zeros of Jacobi Polynomials
Journal of Approximation Theory, 2002 AbstractDenote by xn,k(α,β) and xn,k(λ)=xn,k(λ−1/2,λ−1/2) the zeros, in decreasing order, of the Jacobi polynomial P(α,β)n(x) and of the ultraspherical (Gegenbauer) polynomial Cλn(x), respectively. The monotonicity of xn,k(α,β) as functions of α and β, α,β>−1, is investigated. Necessary conditions such that the zeros of P(a,b)n(x) are smaller (greater)
Dimitrov, D. K., Rodrigues, R. O.
openaire +4 more sources
On linearization coefficients of Jacobi polynomials [PDF]
Applied Mathematics Letters, 2010 AbstractThis article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases, we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger’s and Petkovsek’s algorithms.
Hamza Chaggara, Wolfram Koepf
openaire +1 more source
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 +2 more
doaj +1 more source