Borrow it
 Architecture Library
 Bizzell Memorial Library
 Boorstin Collection
 Chinese Literature Translation Archive
 Engineering Library
 Fine Arts Library
 Harry W. Bass Business History Collection
 History of Science Collections
 John and Mary Nichols Rare Books and Special Collections
 Library Service Center
 Price College Digital Library
 Western History Collections
The Resource Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
Resource Information
The item Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This book gives a new and direct approach into the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of ar bitrary dimensions. Essential parts may even be called elementary because of the chosen techniques. The central topic is the presentation of spherical harmonics in a theory of invariants of the orthogonal group. H. Weyl was one of the first to point out that spherical harmonics must be more than a fortunate guess to simplify numerical computations in mathematical physics. His opinion arose from his occupation with quan tum mechanics and was supported by many physicists. These ideas are the leading theme throughout this treatise. When R. Richberg and I started this project we were surprised, how easy and elegant the general theory could be. One of the highlights of this book is the extension of the classical results of spherical harmonics into the complex. This is particularly important for the complexification of the FunkHecke formula, which is successfully used to introduce orthogonally invariant solutions of the reduced wave equation. The radial parts of these solutions are either Bessel or Hankel functions, which play an important role in the mathematical theory of acoustical and optical waves. These theories often require a detailed analysis of the asymptotic behavior of the solutions. The presented introduction of Bessel and Hankel functions yields directly the leading terms of the asymptotics. Approximations of higher order can be deduced
 Language

 eng
 eng
 Edition
 1st ed. 1998.
 Extent
 1 online resource (VIII, 226 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1 Notations and Basic Theorems>
 1 The General Theory 9
 §2 Primitive Spaces
 §3 The Completeness
 §4 The FunkHecke Formula
 §5 Representations and Interpolations
 §6 Homogeneous Harmonics
 2 The Specific Theories
 §7 The Legendre Polynomials
 §8 The Laplace Integrals
 §9 The Gegenbauer Polynomials
 §10 The Associated Legendre Functions
 §1 The Associated Spaces yjn(q)
 §12 Harmonic Differential Operators
 §13 Maxwell’s Theory of Multipoles
 3 Spherical Harmonics and Differential Equations
 §14 The LaplaceBeltrami Operators
 §15 Spherical Harmonics as Eigenfunctions
 §16 The Legendre Differential Equation
 §17 The Legendre Functions as Hypergeometric Functions
 4 Analysis on the Complex Unit Spheres
 §18 Homogeneous Harmonics in ?q
 §19 Invariant Integrals on S*q1
 §20 Complexification of the FunkHecke Formula
 §21 An Alternative System of Legendre Functions
 5 The Bessel Functions
 §22 Regular Bessel Functions
 §23 Regular Hankel Functions
 §24 Recursive and Asymptotic Relations
 §25 Addition Formulas for Hankel Functions of Order Zero
 §26 Exponential Integrals with Bessel Functions
 §27 The Traditional Notations
 6 Integral Transforms
 §28 Fourier Integrals
 §29 The Fourier Representation Theorem
 §30 The Parseval Identity
 §31 Examples
 7 The Radon Transform
 §32 Radon Transforms and Fourier Transforms
 §33 Radon Transforms and Spherical Symmetries
 §34 The Nicholson Formulas
 8 Appendix
 §35 The ?Function.
 §36 The Hypergeometric Function
 §37 Elementary Asymptotics
 References
 Isbn
 9781461205814
 Label
 Analysis of Spherical Symmetries in Euclidean Spaces
 Title
 Analysis of Spherical Symmetries in Euclidean Spaces
 Statement of responsibility
 by Claus Müller
 Language

 eng
 eng
 Summary
 This book gives a new and direct approach into the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of ar bitrary dimensions. Essential parts may even be called elementary because of the chosen techniques. The central topic is the presentation of spherical harmonics in a theory of invariants of the orthogonal group. H. Weyl was one of the first to point out that spherical harmonics must be more than a fortunate guess to simplify numerical computations in mathematical physics. His opinion arose from his occupation with quan tum mechanics and was supported by many physicists. These ideas are the leading theme throughout this treatise. When R. Richberg and I started this project we were surprised, how easy and elegant the general theory could be. One of the highlights of this book is the extension of the classical results of spherical harmonics into the complex. This is particularly important for the complexification of the FunkHecke formula, which is successfully used to introduce orthogonally invariant solutions of the reduced wave equation. The radial parts of these solutions are either Bessel or Hankel functions, which play an important role in the mathematical theory of acoustical and optical waves. These theories often require a detailed analysis of the asymptotic behavior of the solutions. The presented introduction of Bessel and Hankel functions yields directly the leading terms of the asymptotics. Approximations of higher order can be deduced
 http://library.link/vocab/creatorName
 Müller, Claus
 Dewey number
 515
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 ZvNnpScaHxY
 Image bit depth
 0
 Language note
 English
 LC call number
 QA299.6433
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Applied Mathematical Sciences,
 Series volume
 129
 http://library.link/vocab/subjectName

 Global analysis (Mathematics)
 Geometry
 Chemistry
 Analysis
 Geometry
 Math. Applications in Chemistry
 Theoretical, Mathematical and Computational Physics
 Label
 Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Notations and Basic Theorems>  1 The General Theory 9  §2 Primitive Spaces  §3 The Completeness  §4 The FunkHecke Formula  §5 Representations and Interpolations  §6 Homogeneous Harmonics  2 The Specific Theories  §7 The Legendre Polynomials  §8 The Laplace Integrals  §9 The Gegenbauer Polynomials  §10 The Associated Legendre Functions  §1 The Associated Spaces yjn(q)  §12 Harmonic Differential Operators  §13 Maxwell’s Theory of Multipoles  3 Spherical Harmonics and Differential Equations  §14 The LaplaceBeltrami Operators  §15 Spherical Harmonics as Eigenfunctions  §16 The Legendre Differential Equation  §17 The Legendre Functions as Hypergeometric Functions  4 Analysis on the Complex Unit Spheres  §18 Homogeneous Harmonics in ?q  §19 Invariant Integrals on S*q1  §20 Complexification of the FunkHecke Formula  §21 An Alternative System of Legendre Functions  5 The Bessel Functions  §22 Regular Bessel Functions  §23 Regular Hankel Functions  §24 Recursive and Asymptotic Relations  §25 Addition Formulas for Hankel Functions of Order Zero  §26 Exponential Integrals with Bessel Functions  §27 The Traditional Notations  6 Integral Transforms  §28 Fourier Integrals  §29 The Fourier Representation Theorem  §30 The Parseval Identity  §31 Examples  7 The Radon Transform  §32 Radon Transforms and Fourier Transforms  §33 Radon Transforms and Spherical Symmetries  §34 The Nicholson Formulas  8 Appendix  §35 The ?Function.  §36 The Hypergeometric Function  §37 Elementary Asymptotics  References
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (VIII, 226 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461205814
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461205814
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089188
 (SSID)ssj0001295834
 (PQKBManifestationID)11711502
 (PQKBTitleCode)TC0001295834
 (PQKBWorkID)11347131
 (PQKB)10367223
 (DEHe213)9781461205814
 (MiAaPQ)EBC3075121
 (EXLCZ)993400000000089188
 Label
 Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Notations and Basic Theorems>  1 The General Theory 9  §2 Primitive Spaces  §3 The Completeness  §4 The FunkHecke Formula  §5 Representations and Interpolations  §6 Homogeneous Harmonics  2 The Specific Theories  §7 The Legendre Polynomials  §8 The Laplace Integrals  §9 The Gegenbauer Polynomials  §10 The Associated Legendre Functions  §1 The Associated Spaces yjn(q)  §12 Harmonic Differential Operators  §13 Maxwell’s Theory of Multipoles  3 Spherical Harmonics and Differential Equations  §14 The LaplaceBeltrami Operators  §15 Spherical Harmonics as Eigenfunctions  §16 The Legendre Differential Equation  §17 The Legendre Functions as Hypergeometric Functions  4 Analysis on the Complex Unit Spheres  §18 Homogeneous Harmonics in ?q  §19 Invariant Integrals on S*q1  §20 Complexification of the FunkHecke Formula  §21 An Alternative System of Legendre Functions  5 The Bessel Functions  §22 Regular Bessel Functions  §23 Regular Hankel Functions  §24 Recursive and Asymptotic Relations  §25 Addition Formulas for Hankel Functions of Order Zero  §26 Exponential Integrals with Bessel Functions  §27 The Traditional Notations  6 Integral Transforms  §28 Fourier Integrals  §29 The Fourier Representation Theorem  §30 The Parseval Identity  §31 Examples  7 The Radon Transform  §32 Radon Transforms and Fourier Transforms  §33 Radon Transforms and Spherical Symmetries  §34 The Nicholson Formulas  8 Appendix  §35 The ?Function.  §36 The Hypergeometric Function  §37 Elementary Asymptotics  References
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (VIII, 226 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461205814
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461205814
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089188
 (SSID)ssj0001295834
 (PQKBManifestationID)11711502
 (PQKBTitleCode)TC0001295834
 (PQKBWorkID)11347131
 (PQKB)10367223
 (DEHe213)9781461205814
 (MiAaPQ)EBC3075121
 (EXLCZ)993400000000089188
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/AnalysisofSphericalSymmetriesinEuclidean/PGuyUSXFVJk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/AnalysisofSphericalSymmetriesinEuclidean/PGuyUSXFVJk/">Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/AnalysisofSphericalSymmetriesinEuclidean/PGuyUSXFVJk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/AnalysisofSphericalSymmetriesinEuclidean/PGuyUSXFVJk/">Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>