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Computation Of Spherical Harminics And Approximation By Spherical Harmonic Expansions

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Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions

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Author : W. Freeden
language : en
Publisher:
Release Date : 1985

Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions written by W. Freeden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Geodesy categories.

Spherical Harmonics And Approximations On The Unit Sphere An Introduction

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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-17

Spherical Harmonics And Approximations On The Unit Sphere An Introduction written by Kendall Atkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-17 with Mathematics categories.

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions

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Author : Willi Freeden
language : en
Publisher:
Release Date : 1985

Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions written by Willi Freeden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Gravity categories.

A technique is developed for generating spherical harmonics by exact computation (in integer mode) thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials. Exact computation of (maximal) linearly independent and orthonormal systems of spherical harmonics is explained using exclusively integer operations. The numerical efficiency is discussed. The development of exterior gravitational potential in a series of outer (spherical) harmonics is investigated. Some numerical examples are given for solving exterior Dirichlet's boundary-value problems by use of outer (spherical) harmonic expansions for not-necessarily spherical boundaries. Keywords: Homogeneous harmonic polynomials; Spherical harmonics; Exact computation in integer mode; Series expansion into spherical harmonics; Exterior dirichlet's problem.

Spherical Harmonics In P Dimensions

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Author : Costas Efthimiou
language : en
Publisher: World Scientific
Release Date : 2014-03-07

Spherical Harmonics In P Dimensions written by Costas Efthimiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-07 with Mathematics categories.

The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter.

Hyperspherical Harmonics And Generalized Sturmians

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Author : John S. Avery
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

Hyperspherical Harmonics And Generalized Sturmians written by John S. Avery and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Science categories.

This text explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory and generalized Sturmian basis functions. It also introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation.; The method of many-electron Sturmians offers an interesting alternative to the usual SCF-CI methods for calculating atomic and molecular structure. When many-electron Sturmians are used, and when the basis potential is chosen to be the attractive potential of the nuclei in the system, the following advantages are offered: the matrix representation of the nuclear attraction potential is diagonal; the kinetic energy term vanishes from the secular equation; the Slater exponents of the atomic orbitals are automatically optimized; convergence is rapid; a correlated solution to the many-electron problem can be obtained directly, without the use of the SCF approximation; and excited states can be obtained with good accuracy.; The text should be of interest to advanced students and research workers in theoretical chemistry, physics and mathematics.

Spherical Harmonics

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Author : Claus Müller
language : en
Publisher: Springer
Release Date : 2006-11-14

Spherical Harmonics written by Claus Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.