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We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.

Specializations of one-parameter families of polynomials

Farshid Hajir, Siman Wong (2006)

Annales de l’institut Fourier

Let $K$ be a number field, and suppose $λ (x, t) \in K [x, t]$ is irreducible over $K (t)$ . Using algebraic geometry and group theory, we describe conditions under which the $K$ -exceptional set of $λ$ , i.e. the set of $α \in K$ for which the specialized polynomial $λ (x, α)$ is $K$ -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed $n \geq 10$ , all but finitely many $K$ -specializations of the degree $n$ generalized Laguerre polynomial $L_{n}^{(t)} (x)$ are $K$ -irreducible and have Galois group $S_{n}$ . Second, we study specializations...

Spectra of observables in the $q$ -oscillator and $q$ -analogue of the Fourier transform.

Klimyk, Anatoliy U. (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Spectral Synthesis on Algebras of Orthogonal Polynomial Series.

Matthias Vogel (1987)

Mathematische Zeitschrift

Spline Approximations to Spherically Symmetric Distributions.

Walter Gautschi, G.V. Milovanovic (1986)

Numerische Mathematik

Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method.

Cardoso, J.L., Fernandes, C.M., Álvarez-Nodarse, R. (2009)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

Murugusundaramoorthy, G. (2011)

Mathematica Balkanica New Series

MSC2010: 30C45, 33C45

Sucesiones de polinomios ortogonales estrictamente γ-típicas.

Emilio Torrano, Rafael Guadalupe (1988)

Extracta Mathematicae

Sur les moyennes arithmétiques des suites de fonctions orthogonales

I. S. Gal (1949)

Annales de l'institut Fourier

Soit ${φ_{ν} (x)}$ une suite orthonormale dans l’intervalle $(- \infty < a \leq x \leq b < \infty)$ . L’auteur démontre, que $\sum_{ν = 1}^{N} (1 - \frac{ν - 1}{N}) φ_{ν} (x) = 0 (N^{\frac{1}{2}} (log N)^{\frac{1}{2} + ϵ})$ pour tout $ϵ > 0$ et presque partout dans $a \leq x \leq b$ . La démonstration est basée sur un théorème de MM. Gál et Koksma et on peut généraliser aussi pour le cas $- \infty \leq x \leq \infty$ (théorème auxiliaire). En utilisant ce théorème auxiliaire on obtient tout de suite l’estimation connue pour les fonctions de Lebesgue (théorème 2) [voir Kaczmarcz et Steinhaus, Theorie der Orthogonalreihen, Warszawa, 1935, 577].

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Displaying 381 – 400 of 462

Some remarks on the theory of the Laguerre-Pinney transformation.(Short Communication).

Some results involving a generalized Kampé de Fériet function.

Some results on a generalized $ω$ -Jacobi transform.

Some results on biorthogonal polynomials.

Some results on generating functions.

Some sums of Legendre and Jacobi polynomials

Specializations of one-parameter families of polynomials

Spectra of observables in the $q$ -oscillator and $q$ -analogue of the Fourier transform.

Spectral Synthesis on Algebras of Orthogonal Polynomial Series.

Spline Approximations to Spherically Symmetric Distributions.

Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

Sucesiones de polinomios ortogonales estrictamente γ-típicas.

Sur les moyennes arithmétiques des suites de fonctions orthogonales

Sur quelques relations intégrales entre les solutions de l'équation biconfluente de Heun

Sur une perturbation de la récurrence vérifiée par une suite de polynômes orthogonaux

Systems of orthogonal polynomials defined by hypergeometric type equations.

Szegő polynomials: a view from the Riemann-Hilbert window.

Szegő quadrature and frequency analysis.

The continuous Jacobi transform.

Currently displaying 381 – 400 of 462