Orthogonal polynomials on N-spheres

Gegenbauer, Jacobi, and Heun
  • 21 Pages
  • 4.98 MB
  • English
University of Waikato , Hamilton, N.Z
Statementby E.G. Kalnins and Willard Miller, Jr.
SeriesResearch report ;, ser. 2, no. 5, Research report (University of Waikato. Dept. of Mathematics and Statistics) ;, ser. 2, no. 5.
LC ClassificationsMLCM 93/07303 (Q)
The Physical Object
Pagination21 p. ;
ID Numbers
Open LibraryOL1454557M
LC Control Number93108545

Details Orthogonal polynomials on N-spheres FB2

A New Method for Generating Infinite Sets of Related Sequences of Orthogonal Polynomials, Starting from First-Order Initial-Value Problems (C C Grosjean)Orthogonal Polynomials on n-Spheres: Gegenbauer, Jacobi and Heun (E G Kalnins & W Miller, Jr)Extremal Problems for Polynomials and Their Coefficients (G V Milovanovi et al.).

The n-sphere of unit radius is called the unit n-sphere, denoted S n, often referred to as the n-sphere. When embedded as described, an n-sphere is the surface or boundary of an (n + 1)-dimensional ball. For n ≥ 2, the n-spheres are the simply connected n-dimensional manifolds of constant, positive curvature.

II / J. Wilkins, Jr. --Orthogonal Polynomials of Many Variables and Degenerated Elliptic Equations / A. Yanushauskas --Linear Stationary Second-Degree Methods for the Solution of Large Linear Systems / D.

Young and D. Kincaid --A Theorem on Algebra-Valued Pseudo Polar-Derivatives /. On the Completeness of Orthogonal Polynomials in Left-Definite Sobolev Spaces (W N Everitt et al.) A New Method for Generating Infinite Sets of Related Sequences of Orthogonal Polynomials, Starting from First-Order Initial-Value Problems (C C Grosjean) Orthogonal Polynomials on n-Spheres: Gegenbauer, Jacobi and Heun (E G Kalnins & W Miller, Jr).

Kalnins and W. Miller () Orthogonal Polynomials on n-spheres: Gegenbauer, Jacobi and Heun. In Topics in Polynomials of One and Several Variables and their Applications, pp.

– The space L 2 has the orthogonal decomposition L 2 = 1 M k=0 H k where H k is the space of spherical harmonic polynomials of degree k. It is known that H k has dimension 2k+1. Let fY (k) Gammak. Problems related to the symmetrization of sequences of orthogonal polynomials on the real line play an important role as it is shown in T.

Chihara: “An introduction to orthogonal polynomials. This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications.

It is dedicated to P. Chebyshev, a leading Russian mathematician. Gegenbauer polynomials. In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval with respect to the weight function (1 − x2)α–1/2.

New!!: N-sphere and Gegenbauer polynomials See more» Orthogonal polynomials on N-spheres book measure.

Kalnins and W. Miller, “Orthogonal Polynomials on n-spheres: Gegenbauer, Jacobi and Heun,” in Topics in Polynomials of One and Several Variables and their Applications: A Legacy of P. Chebyshev (–), edited by H.

Srivastava, T. Rassias, and A. Yanushauskas (World Scientific, Singapore, ).Cited by: A note on tensor products of q-algebra representations and orthogonal polynomials, with E.G. Kalnins, Journal of Computational and Applied Mathematics, 68 () PDF Postscript Integrability, Stäckel spaces and rational potentials, with E.G.

Kalnins and S. Benenti, J. Delgado A, Fernández L, Pérez T, Piñar M and Xu Y () Orthogonal polynomials in several variables for measures with mass points, Numerical Algorithms. The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers.

This generalization provides new integral and differential representations in addition to new mathematical results that are useful in theoretical and numerical computations. Inverse-Square Forces and Orthogonal Polynomials Enveloping Circular Arcs Laplace Transforms The Wave Equation and Permutation of Rays Huygens' Principle Recurrence Relations for Ordinary Differential Equations The Curvatures of Hypersurfaces Poisson Processes and Queues The Zeta Function Lagrangian and Hamiltonian Mechanics.

Q&A for professional mathematicians. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. () Computation of scattering from N spheres using multipole reexpansion. The Journal of the Acoustical Society of America() A Cited by: Please read our short guide how to send a book to Kindle.

Save for later. You may be interested in. Most frequently terms. map homotopy homology maps product sequence cohomology theorem spaces proof cell isomorphism hence cells complexes quotient. Zernike polynomials () In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk.

Named after Frits Zernike, the Dutch optical physicist, and the inventor of phase contrast microscopy, they play an important role in beam optics.

Minnaert function (). Abstract. Let J be a system of sets. If all members of J are contained in a given set C and each point of C belongs to at most one member of J then J is said to be a packing into C.

Description Orthogonal polynomials on N-spheres FB2

If, on the other hand, each point of C belongs to at least one member of J then we say that J is a covering of C. Packings and coverings have been considered in various spaces and on various combinatorial by: In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space.

In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Gauss map. Concerning Author: Sun Mi Jung, Young Ho Kim, Jinhua Qian. Two teams of undergraduates participated in the Mathematical Contest in Modeling.

The team of Andrew Harris, Dante Iozzo, and Nigel Michki was designated as "Meritorious Winner" (top 9%) and the team of George Braun, Collin Olander, and Jonathan Tang received honorable mention (top 31%).

John Ringland served as the faculty advisor to both teams. A set of Gegenbauer polynomials {C l λ} builds a complete orthogonal system on [− 1, 1] with weight (1 − t 2) λ − 1 / 2.

Consequently, it is an orthogonal basis for zonal functions on the (2 λ Cited by: Orthogonal Polynomials For use in integration and fitting data by a polynomial, orthogonal polynomials are used. The definition of orthogonal is based on having a set of polynomials from degree 0 to degree n that are denoted by p_0(x), p_1(x),p_n-1(x), p_n(n).

Full text of "Mathematical Sciences, Vol " See other formats. There is also a third book in progress, on vector bundles, characteristic classes, and K–theory, which will be largely independent of [SSAT] and also of much of the present book. This is referred to as [VBKT], its provisional title being ‘Vector Bundles and K–Theory.’ In terms of prerequisites, the present book assumes the reader has.

For a degree list (d) the multi-variate resultant Res (d) is a multi-homogeneous and irreducible diophantine polynomial whose variables are the coefficients of lists f ≔ (f 0,f n) ∈ H (d).

We denote by Res (d) (f 0,f n) or Res (d) (f) the value of the resultant Res (d) at the coefficients of the polynomials in the Cited by: 2. Full text of "A treatise on the circle and sphere" See other formats.

Intrinsic Definition of Orthogonal/Unitary Transformations Can someone point me to a good explanation of the intrinsic definition of an orthogonal/unitary transformation.

By this I mean one which does not make reference to matrices or matrix operations like. Support UT Mathematics, become a donor, Department of Mathematics, The University of Texas at Austin. Deutsch / \\ Trigonometric Symmetries: Four-Dimensional Identities of Modified Chebyshev Polynomials / M.

Dombroski / \\ On the Completeness of Orthogonal Polynomials in Left-Definite Sobolev Spaces / W. Everitt, L. Littlejohn \& R. Wellman / \\ Inequalities for Polynomials and Trigonometric Polynomials Related to the. After a line, the circle is the simplest example of a topological manifold.

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Topology ignores bending, so a small piece of a circle is treated exactly the same as a small piece of a line. Consider, for instance, the top part of the unit circle, x 2 + y 2 = 1, where the y-coordinate is positive (indicated by the yellow circular arc in Figure 1).Any point of this arc can be uniquely described by.Exotic Spheres are related to Division Algebras.

The alternative real division algebras are R, C, Q, and O, the real and complex numbers, quaternions, and octonions, of dimensions 1 = 2^0, 2 = 2^1, 4 = 2^2, and 8 = 2^3 They correspond to the Hopf fibrations of spheres: RP1 -> S1 -> S0 (S1/Z2 can be either RP1 or an orbifold) S1 -> S3 -> S2 S3 -> S7 -> S4 S7 -> S15 -> S8 Their dimensions are.(BGR 4) Suppose medians ma and mb of a triangle are orthogonal.

Prove that: (a) The medians of that triangle correspond to the sides of a right-angled triangle. (b) The inequality 5(a2 + b2 − c2) ≥ 8ab is valid, where a, b, and c are side lengths of the given triangle.