Results 41 to 50 of about 147 (140)

Noise‐Tailored Constructions for Spin Wigner Function Kernels

Advanced Physics Research, Volume 3, Issue 6, June 2024.
This work explores the parameterization of spin Wigner functions to efficiently represent the effects of probabilistic unitary noise on a quantum state. Block diagonalization of the noise operator algebra is used to reduce the required number of parameters while maintaining the Stratonovich–Weyl conditions for the representation.
Michael Hanks, Soovin Lee, M.S. Kim
wiley   +1 more source

Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2019, Issue 1, 2019., 2019
The representation of analytic functions as convergent series in Jacobi polynomials Pn(α,β) is reformulated using the Hadamard principal part of integrals for all α,β∈C∖{01223,-,-,…}, α+β≠-,-,…. The coefficients of the series are given as usual integrals in the classical case (when Rα,Rβ>-1) or by their Hadamard principal part when they diverge.
Rodica D. Costin, Marina David, Shyam L. Kalla   +2 more
wiley   +1 more source

Inequalities Concerning Ultraspherical Polynomials and Bessel Functions [PDF]

Proceedings of the American Mathematical Society, 1950
Presented to the Society, September 7,1948; received by the editors December 28, 1948. 1 This paper was written at the Institute for Numerical Analysis of the National Bureau of Standards, with the financial support of the Office of Naval Research of the U. S. Navy Department. * G. Szego, On an inequality of P.
openaire   +1 more source

Identities for q-Ultraspherical Polynomials and Jacobi Functions [PDF]

Proceedings of the American Mathematical Society, 1995
A q-analogue of a result by Badertscher and Koornwinder [Canad. J. Math. 44 (1992), 750-773] relating the action of a Hahn polynomial of differential operator argument on ultraspherical polynomials to an ultraspherical polynomial of shifted order and degree is derived. The q-analogue involves q-Hahn polynomials, continuous q-ultraspherical polynomials,
openaire   +5 more sources

Multidomain spectral approach to rational‐order fractional derivatives

Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.
Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
wiley   +1 more source

On the Birkhoff Quadrature Formulas Using Even and Odd Order of Derivatives

Mathematical Problems in Engineering, Volume 2015, Issue 1, 2015., 2015
We introduce some New Quadrature Formulas by using Jacoby polynomials and Laguerre polynomials. These formulas can be obtained for a finite and infinite interval and also separately for the even or odd order of derivatives. By using the properties of error functions of the above orthogonal polynomials we can obtain the error functions for these ...
S. Hatami, S. M. Hashemiparast, S. Shateyi, Bing-Jean Lee   +3 more
wiley   +1 more source

An ultraspherical product integration-spectral collocation method for multidimensional partial Volterra integro-differential equations and its convergence analysis

Results in Applied Mathematics
We present a reliable numerical method for solving multidimensional partial Volterra integro-differential equations (PVIDEs). This comprehensive approach integrates techniques from product integration, the Nyström method, and spectral collocation, all ...
Saman Bagherbana, Jafar Biazar, Hossein Aminikhah   +2 more
doaj   +1 more source

Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials

Journal of Applied Mathematics, 2013
Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher
Hee Sun Jung, Ryozi Sakai
doaj   +1 more source

Extremal weight enumerators and ultraspherical polynomials

Discrete Mathematics, 2003
The author establishes an upper bound for the minimum distance of a divisible code in terms of its dual distance, a result that generalizes the Mallows-Sloane bounds for self-dual codes. Moreover, there is a determination of zeta functions for the codes that attain this new bound.
openaire   +1 more source

Differential Equations for Symmetric Generalized Ultraspherical Polynomials [PDF]

Transactions of the American Mathematical Society, 1994
We look for differential equations satisfied by the generalized Jacobi polynomials { P n α , β , M , N ( x ) } n = 0 ∞
openaire   +2 more sources