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Algebraic properties of a family of Jacobi polynomials

John Cullinan, Farshid Hajir, Elizabeth Sell (2009)

Journal de Théorie des Nombres de Bordeaux

The one-parameter family of polynomials is a subfamily of the two-parameter family of Jacobi polynomials. We prove that for each , the polynomial is irreducible over for all but finitely many . If is odd, then with the exception of a finite set of , the Galois group of is ; if is even, then the exceptional set is thin.

Algèbre des fonctions elliptiques et géométrie des ovales cartésiennes

Évelyne Barbin, René Guitart (2001)

Revue d'histoire des mathématiques

Les recherches sur les ovales au xixe témoignent du renouveau des méthodes géométriques et illustrent la mise en concurrence de ces méthodes avec les calculs analytiques. En particulier, elles interviennent dans les relations entre l’algèbre des fonctions elliptiques et la géométrie des courbes, que les mathématiciens pensent en termes d’application ou d’interprétation d’un domaine dans l’autre. La rectification des ovales en arcs d’ellipses est obtenue dans les années 1850 par Roberts et Genocchi,...

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

Luchko, Yury (2008)

Fractional Calculus and Applied Analysis

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...

Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

Troels Roussau Johansen (2011)

Studia Mathematica

The maximal operator S⁎ for the spherical summation operator (or disc multiplier) associated with the Jacobi transform through the defining relation for a function f on ℝ is shown to be bounded from into for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from into . In particular converges almost everywhere towards f, for , whenever (4α + 4)/(2α + 3) < p ≤ 2.

An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret (2010)

Open Mathematics

Zeta-generalized-Euler-constant functions, and defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and (1) = ln , are studied and estimated with high accuracy.

An algebraic addition-theorem for Weierstrass' elliptic function and nomograms

Akira Matsuda (1979)

Aplikace matematiky

A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation , are constructed. In this case, a form of the addition-theorem for Weierstrass’ function involving no derivative is used.

An algorithm for free algebras

Jaroslav Ježek (2010)

Commentationes Mathematicae Universitatis Carolinae

We present an algorithm for constructing the free algebra over a given finite partial algebra in the variety determined by a finite list of equations. The algorithm succeeds whenever the desired free algebra is finite.

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