Results 21 to 30 of about 1,811 (151)
The Viscous and Ohmic Damping of the Earth's Free Core Nutation. [PDF]
J Geophys Res Solid Earth, 2021 Abstract The cause for the damping of the Earth's free core nutation (FCN) and the free inner core nutation eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid ...
Triana SA +4 more
europepmc +2 more sources
Zeros of Jacobi and ultraspherical polynomials [PDF]
The Ramanujan Journal, 2021 Suppose $\{P_{n}^{(α, β)}(x)\}_{n=0}^\infty $ is a sequence of Jacobi polynomials with $ α, β>-1.$ We discuss special cases of a question raised by Alan Sokal at OPSFA in 2019, namely, whether the zeros of $ P_{n}^{(α,β)}(x)$ and $ P_{n+k}^{(α+ t, β+ s )}(x)$ are interlacing if $s,t >0$ and $ k \in \mathbb{N}.$ We consider two cases of this ...
Arvesú, J. +2 more
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Two-dimensional limit series in ultraspherical Jacobi polynomials and their approximative properties [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 Let $C[-1,1]$ be the space of functions continuous on the segment $[-1,1]$, $C[-1,1]^2$ be the space of functions continuous on the square $[-1,1]^2$. We denote by $P_n^\alpha(x)$ the ultraspherical Jacobi polynomials.
Guseinov, Ibraghim G. +1 more
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Sieved Ultraspherical Polynomials [PDF]
Transactions of the American Mathematical Society, 1984 The continuous q q -ultraspherical polynomials contain a number of important examples as limiting or special cases. One of these arose in Allaway’s Ph.D. thesis. In a previous paper we solved a characterization problem essentially equivalent to Allaway’s and showed that these polynomials arose from the q q ...
Al-Salam, Waleed +2 more
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Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices
Studies in Applied Mathematics, Volume 150, Issue 2, Page 420-447, February 2023., 2023 Abstract We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis.
Arieh Iserles, Marcus Webb
wiley +1 more source
Parameter and q asymptotics of Lq‐norms of hypergeometric orthogonal polynomials
International Journal of Quantum Chemistry, Volume 123, Issue 2, January 15, 2023., 2023 The weighted Lq‐norms of orthogonal polynomials are determined when q and the polynomial's parameter tend to infinity. They are given in this work by the leading term of the q and parameter asymptotics of the corresponding quantities of the associated probability density. These results are not only interesting per se, but also because they control many
Nahual Sobrino, Jesus S. Dehesa
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 This article is devoted to deriving a new linearization formula of a class for Jacobi polynomials that generalizes the third‐kind Chebyshev polynomials class. In fact, this new linearization formula generalizes some existing ones in the literature. The derivation of this formula is based on employing a new moment formula of this class of polynomials ...
W. M. Abd-Elhameed +3 more
wiley +1 more source
Algebraic and complexity‐like properties of Jacobi polynomials: Degree and parameter asymptotics
International Journal of Quantum Chemistry, Volume 122, Issue 6, March 15, 2022., 2022 The Cramér–Rao, Fisher–Shannon and LMC complexity‐like measures of the Jacobi polynomials are determined when the polynomial's degree and parameter tend to infinity. They are given by the leading term of the degree and parameter asymptotics of the corresponding statistical properties of the associated probability density.
Nahual Sobrino, Jesus S.‐Dehesa
wiley +1 more source
Orthogonality Property of the Discrete q‐Hermite Matrix Polynomials
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove that the solution of the autonomous q‐difference system DqY(x) = AY(qx) with the initial condition Y(0) = Y0 where A is a constant square complex matrix, Dq is the Jackson q‐derivative and 0 < q < 1, is asymptotically stable if and only if ℜ(λ) < 0 for all λ ∈ σ(A) where σ(A) is the set of all eigenvalues of A (the spectrum of A)
Ahmed Salem +3 more
wiley +1 more source