rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Special Functions of Mathematical (Geo-)Physics
  name:
    name part: Freeden, Willi.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Gutting, Martin.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 501 p. 37 illus., 18 illus. in color. online resource.
  abstract: Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.
  table of contents: 1 Introduction: Geomathematical Motivation -- Part I: Auxiliary Functions -- 2 The Gamma Function -- 3 Orthogonal Polynomials -- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3 -- 5 Vectorial Spherical Harmonics in R^3 -- 6 Spherical Harmonics in R^q -- 7 Classical Bessel Functions -- 8 Bessel Functions in R^q -- Part III: Periodically Oriented Functions -- 9 Lattice Functions in R -- 10 Lattice Functions in R^q -- 11 Concluding Remarks -- References -- Index.
  note: by Willi Freeden, Martin Gutting.
  subject:
    topic: Mathematics
  subject:
    topic: Geophysics
  subject:
    topic: Atmospheric sciences
  subject:
    topic: Harmonic analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Special functions
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Special Functions
  subject:
    topic: Mathematical Physics
  subject:
    topic: Geophysics/Geodesy
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Abstract Harmonic Analysis
  subject:
    topic: Atmospheric Sciences
  classification: QA351
  classification: 515.5
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Applied and Numerical Harmonic Analysis
  identifier: 9783034805636
  identifier: http://dx.doi.org/10.1007/978-3-0348-0563-6
  record info:
    record creation date: 130217
    record change date: 20151204174146.0
    record identifier: 978-3-0348-0563-6