Results 61 to 70 of about 1,811 (151)

A Review of Certain Modern Special Functions and Their Applications

Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed, Mohamed Abdalla, AbdelMaksoud Soliman   +2 more
wiley   +1 more source

Time Varying Isotropic Vector Random Fields on Spheres

, 2016
For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which ...
Ma, Chunsheng
core   +1 more source

Extremal Properties of Ultraspherical Polynomials

Journal of Approximation Theory, 1994
It is known that among all polynomials \(P_ n(x)= \sum_{j\equiv 0}^ n a_ j x^ j\) satisfying \(\max_{-1\leq x\leq 1} | P_ n (x)|\leq 1\), the \(\max | a_ n|\) is obtained for the Chebyshev polynomials \(T_ n(x)\) of the first kind. Similarly, \(U_ n(x)\) maximizes \(| a_ n|\) among all polynomials \(P_ n(x)\) satisfying \(\max_{-1\leq x\leq 1} \sqrt{1-
openaire   +2 more sources

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
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

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

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