Computation Of Spherical Harmonics 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.
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 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 Harminics And Approximation By Spherical Harmonic Expansions
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Author : W. Freeden
language : en
Publisher:
Release Date : 1985
Computation Of Spherical Harminics 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 categories.
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.
The Theory Of Potential And Spherical Harmonics
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Author : Wolfgang J. Sternberg
language : en
Publisher:
Release Date : 1952
The Theory Of Potential And Spherical Harmonics written by Wolfgang J. Sternberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Harmonic analysis categories.
Hyperspherical Harmonics
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Author : John S. Avery
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hyperspherical Harmonics 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 2012-12-06 with Science categories.
where d 3 3)2 ( L x - -- i3x j3x j i i>j Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3-dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a d-dimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (3-27»: The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A , chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3-dimensional space. Similarly, one finds that a d-dimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations ( 4 - 27) and ( 4 - 30) ) : 00 ik·x e = (d-4)!!A~oiA(d+2A-2)j~(kr)C~(~k'~) 00 (d-2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O ). l). l)J where I(O) is the total solid angle. This expansion of a d-dimensional plane wave is useful when we wish to calculate Fourier transforms in a d-dimensional space.
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.
The Theory Of Spherical And Ellipsoidal Harmonics
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Author : E. W. Hobson
language : en
Publisher: CUP Archive
Release Date :
The Theory Of Spherical And Ellipsoidal Harmonics written by E. W. Hobson and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Harmonic Analysis And Approximation On The Unit Sphere
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Author : Kunyang Wang
language : en
Publisher:
Release Date : 2000
Harmonic Analysis And Approximation On The Unit Sphere written by Kunyang Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Approximation theory categories.